{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_15207/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_15207","id":"gutenberg_15207","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/15207","summary":null,"tags":["Category: Philosophy & Ethics","Category: Science - Physics","Physics"],"text":"E-text prepared by Jeff Spirko, Juliet Sutherland, Jim Land, and the\nProject Gutenberg Online Distributed Proofreading Team\n\n\n\nThe International Scientific Series\n\nTHE NEW PHYSICS AND ITS EVOLUTION\n\nby\n\nLUCIEN POINCARE\nInspecteur-General de l'Instruction Publique\n\nBeing the Authorized Translation of _LA PHYSIQUE MODERNE, SON EVOLUTION_\n\nNew York\nD. Appleton and Company\n\n1909\n\n\n\n\n\n\n\nPrefatory Note\n\nM. Lucien Poincare is one of the distinguished family of\nmathematicians which has during the last few years given a\nMinister of Finance to the Republic and a President to the\nAcademie des Sciences. He is also one of the nineteen\nInspectors-General of Public Instruction who are charged with the\nduty of visiting the different universities and _lycees_ in\nFrance and of reporting upon the state of the studies there\npursued. Hence he is in an excellent position to appreciate at\nits proper value the extraordinary change which has lately\nrevolutionized physical science, while his official position has\nkept him aloof from the controversies aroused by the discovery of\nradium and by recent speculations on the constitution of matter.\n\nM. Poincare's object and method in writing the book are\nsufficiently explained in the preface which follows; but it may\nbe remarked that the best of methods has its defects, and the\nexcessive condensation which has alone made it possible to\ninclude the last decade's discoveries in physical science within\na compass of some 300 pages has, perhaps, made the facts here\nnoted assimilable with difficulty by the untrained reader. To\nremedy this as far as possible, I have prefixed to the present\ntranslation a table of contents so extended as to form a fairly\ncomplete digest of the book, while full indexes of authors and\nsubjects have also been added. The few notes necessary either for\nbetter elucidation of the terms employed, or for giving account\nof discoveries made while these pages were passing through the\npress, may be distinguished from the author's own by the\nsignature \"ED.\"\n\nTHE EDITOR.\n\nROYAL INSTITUTION OF GREAT BRITAIN,\nApril 1907.\n\n\n\n\nAuthor's Preface\n\nDuring the last ten years so many works have accumulated in the\ndomain of Physics, and so many new theories have been propounded,\nthat those who follow with interest the progress of science, and\neven some professed scholars, absorbed as they are in their own\nspecial studies, find themselves at sea in a confusion more\napparent than real.\n\nIt has therefore occurred to me that it might be useful to write\na book which, while avoiding too great insistence on purely\ntechnical details, should try to make known the general results\nat which physicists have lately arrived, and to indicate the\ndirection and import which should be ascribed to those\nspeculations on the constitution of matter, and the discussions\non the nature of first principles, to which it has become, so to\nspeak, the fashion of the present day to devote oneself.\n\nI have endeavoured throughout to rely only on the experiments in\nwhich we can place the most confidence, and, above all, to show\nhow the ideas prevailing at the present day have been formed, by\ntracing their evolution, and rapidly examining the successive\ntransformations which have brought them to their present\ncondition.\n\nIn order to understand the text, the reader will have no need to\nconsult any treatise on physics, for I have throughout given the\nnecessary definitions and set forth the fundamental facts.\nMoreover, while strictly employing exact expressions, I have\navoided the use of mathematical language. Algebra is an admirable\ntongue, but there are many occasions where it can only be used\nwith much discretion.\n\nNothing would be easier than to point out many great omissions\nfrom this little volume; but some, at all events, are not\ninvoluntary.\n\nCertain questions which are still too confused have been put on\none side, as have a few others which form an important collection\nfor a special study to be possibly made later. Thus, as regards\nelectrical phenomena, the relations between electricity and\noptics, as also the theories of ionization, the electronic\nhypothesis, etc., have been treated at some length; but it has\nnot been thought necessary to dilate upon the modes of production\nand utilization of the current, upon the phenomena of magnetism,\nor upon all the applications which belong to the domain of\nElectrotechnics.\n\nL. POINCARE.\n\n\n\n\n\nContents\n\n\nEDITOR'S PREFATORY NOTE\n\nAUTHOR'S PREFACE\n\nTABLE OF CONTENTS\n\n\nCHAPTER I\n\nTHE EVOLUTION OF PHYSICS\n\nRevolutionary change in modern Physics only apparent:\nevolution not revolution the rule in Physical Theory--\nRevival of metaphysical speculation and influence of\nDescartes: all phenomena reduced to matter and movement--\nModern physicists challenge this: physical, unlike\nmechanical, phenomena seldom reversible--Two schools,\none considering experimental laws imperative, the other\nmerely studying relations of magnitudes: both teach\nsomething of truth--Third or eclectic school--\nIs mechanics a branch of electrical science?\n\n\nCHAPTER II\n\nMEASUREMENTS\n\nSec. 1. Metrology: Lord Kelvin's view of its necessity--\nIts definition\n\nSec. 2. The Measure of Length: Necessity for unit--\nAbsolute length--History of Standard--Description of\nStandard Metre--Unit of wave-lengths preferable--The\nInternational Metre\n\nSec. 3. The Measure of Mass: Distinction between\nmass and weight--Objections to legal kilogramme\nand its precision--Possible improvement\n\nSec. 4. The Measure of Time: Unit of time the\nsecond--Alternative units proposed--Improvements in\nchronometry and invar\n\nSec. 5. The Measure of Temperature: Fundamental\nand derived units--Ordinary unit of temperature\npurely arbitrary--Absolute unit mass of H at pressure\nof 1 m. of Hg at 0 deg. C.--Divergence of thermometric\nand thermodynamic scales--Helium thermometer for low,\nthermo-electric couple for high, temperatures--Lummer\nand Pringsheim's improvements in thermometry.\n\nSec. 6. Derived Units and Measure of Energy:\nImportance of erg as unit--Calorimeter usual means of\ndetermination--Photometric units.\n\nSec. 7. Measure of Physical Constants: Constant of\ngravitation--Discoveries of Cavendish, Vernon Boys,\nEoetvoes, Richarz and Krigar-Menzel--Michelson's\nimprovements on Fizeau and Foucault's experiments--\nMeasure of speed of light.\n\n\nCHAPTER III\n\nPRINCIPLES\n\nSec. 1. The Principles of Physics: The Principles of\nMechanics affected by recent discoveries--Is mass\nindestructible?--Landolt and Heydweiller's experiments\n--Lavoisier's law only approximately true--Curie's\nprinciple of symmetry.\n\nSec. 2. The Principle of the Conservation of Energy:\nIts evolution: Bernoulli, Lavoisier and Laplace, Young,\nRumford, Davy, Sadi Carnot, and Robert Mayer--Mayer's\ndrawbacks--Error of those who would make mechanics part\nof energetics--Verdet's predictions--Rankine inventor\nof energetics--Usefulness of Work as standard form of\nenergy--Physicists who think matter form of energy--\nObjections to this--Philosophical value of conservation\ndoctrine.\n\nSec. 3. The Principle of Carnot and Clausius:\nOriginality of Carnot's principle that fall of\ntemperature necessary for production of work by heat--\nClausius' postulate that heat cannot pass from cold to\nhot body without accessory phenomena--Entropy result\nof this--Definition of entropy--Entropy tends to increase\nincessantly--A magnitude which measures evolution\nof system--Clausius' and Kelvin's deduction that\nheat end of all energy in Universe--Objection to this--\nCarnot's principle not necessarily referable to mechanics\n--Brownian movements--Lippmann's objection to\nkinetic hypothesis.\n\nSec. 4. Thermodynamics: Historical work of Massieu,\nWillard Gibbs, Helmholtz, and Duhem--Willard Gibbs\nfounder of thermodynamic statics, Van t'Hoff its\nreviver--The Phase Law--Raveau explains it without\nthermodynamics.\n\nSec. 5. Atomism: Connection of subject with preceding\nHannequin's essay on the atomic hypothesis--Molecular\nphysics in disfavour--Surface-tension, etc., vanishes\nwhen molecule reached--Size of molecule--Kinetic\ntheory of gases--Willard Gibbs and Boltzmann introduce\ninto it law of probabilities--Mean free path of gaseous\nmolecules--Application to optics--Final division of\nmatter.\n\n\nCHAPTER IV\n\nTHE VARIOUS STATES OF MATTER\n\nSec. 1. The Statics of Fluids: Researches of Andrews,\nCailletet, and others on liquid and gaseous states--\nAmagat's experiments--Van der Waals' equation--Discovery\nof corresponding states--Amagat's superposed\ndiagrams--Exceptions to law--Statics of mixed fluids--\nKamerlingh Onnes' researches--Critical Constants--\nCharacteristic equation of fluid not yet ascertainable.\n\nSec. 2. The Liquefaction of Gases and Low Temperatures:\nLinde's, Siemens', and Claude's methods of liquefying\ngases--Apparatus of Claude described--Dewar's\nexperiments--Modification of electrical properties of\nmatter by extreme cold: of magnetic and chemical--\nVitality of bacteria unaltered--Ramsay's discovery\nof rare gases of atmosphere--Their distribution in\nnature--Liquid hydrogen--Helium.\n\nSec. 3. Solids and Liquids: Continuity of Solid and Liquid\nStates--Viscosity common to both--Also Rigidity--\nSpring's analogies of solids and liquids--Crystallization\n--Lehmann's liquid crystals--Their existence doubted\n--Tamman's view of discontinuity between crystalline\nand liquid states.\n\nSec. 4. The Deformation of Solids: Elasticity--\nHoocke's, Bach's, and Bouasse's researches--Voigt\non the elasticity of crystals--Elastic and permanent\ndeformations--Brillouin's states of unstable\nequilibria--Duhem and the thermodynamic postulates--\nExperimental confirmation--Guillaume's researches\non nickel steel--Alloys.\n\n\nCHAPTER V\n\nSOLUTIONS AND ELECTROLYTIC DISSOCIATION\n\nSec. 1. Solution: Kirchhoff's, Gibb's, Duhem's and Van\nt'Hoff's researches.\n\nSec. 2. Osmosis: History of phenomenon--Traube and\nbiologists establish existence of semi-permeable\nwalls--Villard's experiments with gases--Pfeffer\nshows osmotic pressure proportional to concentration--\nDisagreement as to cause of phenomenon.\n\nSec. 3. Osmosis applied to Solution: Van t'Hoff's\ndiscoveries--Analogy between dissolved body and\nperfect gas--Faults in analogy.\n\nSec. 4. Electrolytic Dissociation: Van t'Hoff's and\nArrhenius' researches--Ionic hypothesis of--Fierce\nopposition to at first--Arrhenius' ideas now triumphant\n--Advantages of Arrhenius' hypothesis--\"The ions\nwhich react\"--Ostwald's conclusions from this--Nernst's\ntheory of Electrolysis--Electrolysis of gases makes\nelectronic theory probable--Faraday's two laws--Valency--\nHelmholtz's consequences from Faraday's laws.\n\n\nCHAPTER VI\n\nTHE ETHER\n\nSec. 1. The Luminiferous Ether: First idea of Ether due\nto Descartes--Ether must be imponderable--Fresnel shows\nlight vibrations to be transverse--Transverse vibrations\ncannot exist in fluid--Ether must be discontinuous.\n\nSec. 2. Radiations: Wave-lengths and their\nmeasurements--Rubens' and Lenard's researches--\nStationary waves and colour-photography--Fresnel's\nhypothesis opposed by Neumann--Wiener's and Cotton's\nexperiments.\n\nSec. 3. The Electromagnetic Ether: Ampere's advocacy\nof mathematical expression--Faraday first shows\ninfluence of medium in electricity--Maxwell's proof\nthat light-waves electromagnetic--His\nunintelligibility--Required confirmation of theory by Hertz.\n\nSec. 4. Electrical Oscillations: Hertz's experiments--\nBlondlot proves electromagnetic disturbance propagated\nwith speed of light--Discovery of ether waves\nintermediate between Hertzian and visible ones--Rubens'\nand Nichols' experiments--Hertzian and light rays\ncontrasted--Pressure of light.\n\nSec. 5. The X-Rays: Roentgen's discovery--Properties\nof X-rays--Not homogeneous--Rutherford and M'Clung's\nexperiments on energy corresponding to--Barkla's\nexperiments on polarisation of--Their speed that of\nlight--Are they merely ultra-violet?--Stokes and\nWiechert's theory of independent pulsations generally\npreferred--J.J. Thomson's idea of their formation--\nSutherland's and Le Bon's theories--The N-Rays--\nBlondlot's discovery--Experiments cannot be repeated\noutside France--Gutton and Mascart's confirmation--\nNegative experiments prove nothing--Supposed\nwave-length of N-rays.\n\nSec. 6. The Ether and Gravitation: Descartes'\nand Newton's ideas on gravitation--Its speed and\nother extraordinary characteristics--Lesage's\nhypothesis--Cremieux' experiments with drops of\nliquids--Hypothesis of ether insufficient.\n\n\nCHAPTER VII\n\nWIRELESS TELEGRAPHY\n\nSec. 1. Histories of wireless telegraphy already written,\nand difficulties of the subject.\n\nSec. 2. Two systems: that which uses the material media (earth,\nair, or water), and that which employs ether only.\n\nSec. 3. Use of earth as return wire by Steinheil\n--Morse's experiments with water of canal--Seine used as\nreturn wire during siege of Paris--Johnson and Melhuish's\nIndian experiments--Preece's telegraph over Bristol\nChannel--He welcomes Marconi.\n\nSec. 4. Early attempts at transmission of messages through\nether--Experiments of Rathenau and others.\n\nSec. 5. Forerunners of ether telegraphy: Clerk Maxwell\nand Hertz--Dolbear, Hughes, and Graham Bell.\n\nSec. 6. Telegraphy by Hertzian waves first suggested\nby Threlfall--Crookes', Tesla's, Lodge's,\nRutherford's, and Popoff's contributions--Marconi\nfirst makes it practicable.\n\nSec. 7. The receiver in wireless telegraphy--Varley's,\nCalzecchi--Onesti's, and Branly's researches--\nExplanation of coherer still obscure.\n\nSec. 8. Wireless telegraphy enters the commercial stage--\nDefect of Marconi's system--Braun's, Armstrong's, Lee de\nForest's, and Fessenden's systems make use of earth--\nHertz and Marconi entitled to foremost place among\ndiscoverers.\n\n\nCHAPTER VIII\n\nTHE CONDUCTIVITY OF GASES AND THE IONS\n\nSec. 1. The Conductivity of Gases: Relations of matter to\nether cardinal problem--Conductivity of gases at first\nmisapprehended--Erman's forgotten researches--Giese\nfirst notices phenomenon--Experiment with X-rays--\nJ.J. Thomson's interpretation--Ionized gas not obedient\nto Ohm's law--Discharge of charged conductors by\nionized gas.\n\nSec. 2. The Condensation of water-vapour by Ions:\nVapour will not condense without nucleus--Wilson's\nexperiments on electrical condensation--Wilson and\nThomson's counting experiment--Twenty million ions\nper c.cm. of gas--Estimate of charge borne by ion--\nSpeed of charges--Zeleny's and Langevin's\nexperiments--Negative ions 1/1000 of size of\natoms--Natural unit of electricity or electrons.\n\nSec. 3. How Ions are Produced: Various causes\nof ionization--Moreau's experiments with alkaline\nsalts--Barus and Bloch on ionization by phosphorus\nvapours--Ionization always result of shock.\n\nSec. 4. Electrons in Metals: Movement of\nelectrons in metals foreshadowed by Weber--Giese's,\nRiecke's, Drude's, and J.J. Thomson's researches--Path\nof ions in metals and conduction of heat--Theory of\nLorentz--Hesehus' explanation of electrification by\ncontact--Emission of electrons by charged body--\nThomson's measurement of positive ions.\n\n\nCHAPTER IX\n\nCATHODE RAYS AND RADIOACTIVE BODIES\n\nSec. 1. The Cathode Rays: History of discovery--Crookes'\ntheory--Lenard rays--Perrin's proof of negative\ncharge--Cathode rays give rise to X-rays--The canal\nrays--Villard's researches and magneto-cathode rays--\nIonoplasty--Thomson's measurements of speed of rays--\nAll atoms can be dissociated.\n\nSec. 2. Radioactive Substances: Uranic rays of Niepce\nde St Victor and Becquerel--General radioactivity of\nmatter--Le Bon's and Rutherford's comparison of uranic\nwith X rays--Pierre and Mme. Curie's discovery of\npolonium and radium--Their characteristics--Debierne\ndiscovers actinium.\n\nSec. 3. Radiations and Emanations of Radioactive\nBodies: Giesel's, Becquerel's, and Rutherford's\nResearches--Alpha, beta, and gamma rays--Sagnac's\nsecondary rays--Crookes' spinthariscope--The emanation\n--Ramsay and Soddy's researches upon it--Transformations\nof radioactive bodies--Their order.\n\nSec. 4. Disaggregation of Matter and Atomic Energy:\nActual transformations of matter in radioactive bodies\n--Helium or lead final product--Ultimate disappearance\nof radium from earth--Energy liberated by radium:\nits amount and source--Suggested models of radioactive\natoms--Generalization from radioactive phenomena\n-Le Bon's theories--Ballistic hypothesis generally\nadmitted--Does energy come from without--Sagnac's\nexperiments--Elster and Geitel's _contra_.\n\n\nCHAPTER X\n\nTHE ETHER AND MATTER\n\nSec. 1. The Relations between the Ether and Matter:\nAttempts to reduce all matter to forms of ether--Emission\nand absorption phenomena show reciprocal action--\nLaws of radiation--Radiation of gases--Production of\nspectrum--Differences between light and sound variations\nshow difference of media--Cauchy's, Briot's, Carvallo's\nand Boussinesq's researches--Helmholtz's and\nPoincare's electromagnetic theories of dispersion.\n\nSec. 2. The Theory of Lorentz:--Mechanics fails\nto explain relations between ether and matter--Lorentz\npredicts action of magnet on spectrum--Zeeman's experiment\n--Later researches upon Zeeman effect--\nMultiplicity of electrons--Lorentz's explanation of\nthermoelectric phenomena by electrons--Maxwell's and\nLorentz's theories do not agree--Lorentz's probably more\ncorrect--Earth's movement in relation to ether.\n\nSec. 3. The Mass of Electrons: Thomson's and\nMax Abraham's view that inertia of charged body due\nto charge--Longitudinal and transversal mass--Speed\nof electrons cannot exceed that of light--Ratio of\ncharge to mass and its variation--Electron simple\nelectric charge--Phenomena produced by its acceleration.\n\nSec. 4. New Views on Ether and Matter:\nInsufficiency of Larmor's view--Ether definable\nby electric and magnetic fields--Is matter all electrons?\nAtom probably positive centre surrounded by\nnegative electrons--Ignorance concerning positive\nparticles--Successive transformations of matter probable\n--Gravitation still unaccounted for.\n\n\nCHAPTER XI\n\nTHE FUTURE OF PHYSICS\n\nPersistence of ambition to discover supreme principle\nin physics--Supremacy of electron theory at present\ntime--Doubtless destined to disappear like others--\nConstant progress of science predicted--Immense field\nopen before it.\n\nINDEX OF NAMES\n\nINDEX OF SUBJECTS\n\n\n\n\nCHAPTER I\n\nTHE EVOLUTION OF PHYSICS\n\n\nThe now numerous public which tries with some success to keep abreast\nof the movement in science, from seeing its mental habits every day\nupset, and from occasionally witnessing unexpected discoveries that\nproduce a more lively sensation from their reaction on social life, is\nled to suppose that we live in a really exceptional epoch, scored by\nprofound crises and illustrated by extraordinary discoveries, whose\nsingularity surpasses everything known in the past. Thus we often hear\nit said that physics, in particular, has of late years undergone a\nveritable revolution; that all its principles have been made new, that\nall the edifices constructed by our fathers have been overthrown, and\nthat on the field thus cleared has sprung up the most abundant harvest\nthat has ever enriched the domain of science.\n\nIt is in fact true that the crop becomes richer and more fruitful,\nthanks to the development of our laboratories, and that the quantity\nof seekers has considerably increased in all countries, while their\nquality has not diminished. We should be sustaining an absolute\nparadox, and at the same time committing a crying injustice, were we\nto contest the high importance of recent progress, and to seek to\ndiminish the glory of contemporary physicists. Yet it may be as well\nnot to give way to exaggerations, however pardonable, and to guard\nagainst facile illusions. On closer examination it will be seen that\nour predecessors might at several periods in history have conceived,\nas legitimately as ourselves, similar sentiments of scientific pride,\nand have felt that the world was about to appear to them transformed\nand under an aspect until then absolutely unknown.\n\nLet us take an example which is salient enough; for, however arbitrary\nthe conventional division of time may appear to a physicist's eyes, it\nis natural, when instituting a comparison between two epochs, to\nchoose those which extend over a space of half a score of years, and\nare separated from each other by the gap of a century. Let us, then,\ngo back a hundred years and examine what would have been the state of\nmind of an erudite amateur who had read and understood the chief\npublications on physical research between 1800 and 1810.\n\nLet us suppose that this intelligent and attentive spectator witnessed\nin 1800 the discovery of the galvanic battery by Volta. He might from\nthat moment have felt a presentiment that a prodigious transformation\nwas about to occur in our mode of regarding electrical phenomena.\nBrought up in the ideas of Coulomb and Franklin, he might till then\nhave imagined that electricity had unveiled nearly all its mysteries,\nwhen an entirely original apparatus suddenly gave birth to\napplications of the highest interest, and excited the blossoming of\ntheories of immense philosophical extent.\n\nIn the treatises on physics published a little later, we find traces\nof the astonishment produced by this sudden revelation of a new world.\n\"Electricity,\" wrote the Abbe Hauey, \"enriched by the labour of so many\ndistinguished physicists, seemed to have reached the term when a\nscience has no further important steps before it, and only leaves to\nthose who cultivate it the hope of confirming the discoveries of their\npredecessors, and of casting a brighter light on the truths revealed.\nOne would have thought that all researches for diversifying the\nresults of experiment were exhausted, and that theory itself could\nonly be augmented by the addition of a greater degree of precision to\nthe applications of principles already known. While science thus\nappeared to be making for repose, the phenomena of the convulsive\nmovements observed by Galvani in the muscles of a frog when connected\nby metal were brought to the attention and astonishment of\nphysicists.... Volta, in that Italy which had been the cradle of the\nnew knowledge, discovered the principle of its true theory in a fact\nwhich reduces the explanation of all the phenomena in question to the\nsimple contact of two substances of different nature. This fact became\nin his hands the germ of the admirable apparatus to which its manner\nof being and its fecundity assign one of the chief places among those\nwith which the genius of mankind has enriched physics.\"\n\nShortly afterwards, our amateur would learn that Carlisle and\nNicholson had decomposed water by the aid of a battery; then, that\nDavy, in 1803, had produced, by the help of the same battery, a quite\nunexpected phenomenon, and had succeeded in preparing metals endowed\nwith marvellous properties, beginning with substances of an earthy\nappearance which had been known for a long time, but whose real nature\nhad not been discovered.\n\nIn another order of ideas, surprises as prodigious would wait for our\namateur. Commencing with 1802, he might have read the admirable series\nof memoirs which Young then published, and might thereby have learned\nhow the study of the phenomena of diffraction led to the belief that\nthe undulation theory, which, since the works of Newton seemed\nirretrievably condemned, was, on the contrary, beginning quite a new\nlife. A little later--in 1808--he might have witnessed the discovery\nmade by Malus of polarization by reflexion, and would have been able\nto note, no doubt with stupefaction, that under certain conditions a\nray of light loses the property of being reflected.\n\nHe might also have heard of one Rumford, who was then promulgating\nvery singular ideas on the nature of heat, who thought that the then\nclassical notions might be false, that caloric does not exist as a\nfluid, and who, in 1804, even demonstrated that heat is created by\nfriction. A few years later he would learn that Charles had enunciated\na capital law on the dilatation of gases; that Pierre Prevost, in\n1809, was making a study, full of original ideas, on radiant heat. In\nthe meantime he would not have failed to read volumes iii. and iv. of\nthe _Mecanique celeste_ of Laplace, published in 1804 and 1805, and he\nmight, no doubt, have thought that before long mathematics would\nenable physical science to develop with unforeseen safety.\n\nAll these results may doubtless be compared in importance with the\npresent discoveries. When strange metals like potassium and sodium\nwere isolated by an entirely new method, the astonishment must have\nbeen on a par with that caused in our time by the magnificent\ndiscovery of radium. The polarization of light is a phenomenon as\nundoubtedly singular as the existence of the X rays; and the upheaval\nproduced in natural philosophy by the theories of the disintegration\nof matter and the ideas concerning electrons is probably not more\nconsiderable than that produced in the theories of light and heat by\nthe works of Young and Rumford.\n\nIf we now disentangle ourselves from contingencies, it will be\nunderstood that in reality physical science progresses by evolution\nrather than by revolution. Its march is continuous. The facts which\nour theories enable us to discover, subsist and are linked together\nlong after these theories have disappeared. Out of the materials of\nformer edifices overthrown, new dwellings are constantly being\nreconstructed.\n\nThe labour of our forerunners never wholly perishes. The ideas of\nyesterday prepare for those of to-morrow; they contain them, so to\nspeak, _in potentia_. Science is in some sort a living organism, which\ngives birth to an indefinite series of new beings taking the places of\nthe old, and which evolves according to the nature of its environment,\nadapting itself to external conditions, and healing at every step the\nwounds which contact with reality may have occasioned.\n\nSometimes this evolution is rapid, sometimes it is slow enough; but it\nobeys the ordinary laws. The wants imposed by its surroundings create\ncertain organs in science. The problems set to physicists by the\nengineer who wishes to facilitate transport or to produce better\nillumination, or by the doctor who seeks to know how such and such a\nremedy acts, or, again, by the physiologist desirous of understanding\nthe mechanism of the gaseous and liquid exchanges between the cell and\nthe outer medium, cause new chapters in physics to appear, and suggest\nresearches adapted to the necessities of actual life.\n\nThe evolution of the different parts of physics does not, however,\ntake place with equal speed, because the circumstances in which they\nare placed are not equally favourable. Sometimes a whole series of\nquestions will appear forgotten, and will live only with a languishing\nexistence; and then some accidental circumstance suddenly brings them\nnew life, and they become the object of manifold labours, engross\npublic attention, and invade nearly the whole domain of science.\n\nWe have in our own day witnessed such a spectacle. The discovery of\nthe X rays--a discovery which physicists no doubt consider as the\nlogical outcome of researches long pursued by a few scholars working\nin silence and obscurity on an otherwise much neglected subject--\nseemed to the public eye to have inaugurated a new era in the history\nof physics. If, as is the case, however, the extraordinary scientific\nmovement provoked by Roentgen's sensational experiments has a very\nremote origin, it has, at least, been singularly quickened by the\nfavourable conditions created by the interest aroused in its\nastonishing applications to radiography.\n\nA lucky chance has thus hastened an evolution already taking place,\nand theories previously outlined have received a singular development.\nWithout wishing to yield too much to what may be considered a whim of\nfashion, we cannot, if we are to note in this book the stage actually\nreached in the continuous march of physics, refrain from giving a\nclearly preponderant place to the questions suggested by the study of\nthe new radiations. At the present time it is these questions which\nmove us the most; they have shown us unknown horizons, and towards the\nfields recently opened to scientific activity the daily increasing\ncrowd of searchers rushes in rather disorderly fashion.\n\nOne of the most interesting consequences of the recent discoveries has\nbeen to rehabilitate in the eyes of scholars, speculations relating to\nthe constitution of matter, and, in a more general way, metaphysical\nproblems. Philosophy has, of course, never been completely separated\nfrom science; but in times past many physicists dissociated themselves\nfrom studies which they looked upon as unreal word-squabbles, and\nsometimes not unreasonably abstained from joining in discussions which\nseemed to them idle and of rather puerile subtlety. They had seen the\nruin of most of the systems built up _a priori_ by daring\nphilosophers, and deemed it more prudent to listen to the advice given\nby Kirchhoff and \"to substitute the description of facts for a sham\nexplanation of nature.\"\n\nIt should however be remarked that these physicists somewhat deceived\nthemselves as to the value of their caution, and that the mistrust\nthey manifested towards philosophical speculations did not preclude\ntheir admitting, unknown to themselves, certain axioms which they did\nnot discuss, but which are, properly speaking, metaphysical\nconceptions. They were unconsciously speaking a language taught them\nby their predecessors, of which they made no attempt to discover the\norigin. It is thus that it was readily considered evident that physics\nmust necessarily some day re-enter the domain of mechanics, and thence\nit was postulated that everything in nature is due to movement. We,\nfurther, accepted the principles of the classical mechanics without\ndiscussing their legitimacy.\n\nThis state of mind was, even of late years, that of the most\nillustrious physicists. It is manifested, quite sincerely and without\nthe slightest reserve, in all the classical works devoted to physics.\nThus Verdet, an illustrious professor who has had the greatest and\nmost happy influence on the intellectual formation of a whole\ngeneration of scholars, and whose works are even at the present day\nvery often consulted, wrote: \"The true problem of the physicist is\nalways to reduce all phenomena to that which seems to us the simplest\nand clearest, that is to say, to movement.\" In his celebrated course\nof lectures at l'Ecole Polytechnique, Jamin likewise said: \"Physics\nwill one day form a chapter of general mechanics;\" and in the preface\nto his excellent course of lectures on physics, M. Violle, in 1884,\nthus expresses himself: \"The science of nature tends towards mechanics\nby a necessary evolution, the physicist being able to establish solid\ntheories only on the laws of movement.\" The same idea is again met\nwith in the words of Cornu in 1896: \"The general tendency should be to\nshow how the facts observed and the phenomena measured, though first\nbrought together by empirical laws, end, by the impulse of successive\nprogressions, in coming under the general laws of rational mechanics;\"\nand the same physicist showed clearly that in his mind this connexion\nof phenomena with mechanics had a deep and philosophical reason, when,\nin the fine discourse pronounced by him at the opening ceremony of the\nCongres de Physique in 1900, he exclaimed: \"The mind of Descartes\nsoars over modern physics, or rather, I should say, he is their\nluminary. The further we penetrate into the knowledge of natural\nphenomena, the clearer and the more developed becomes the bold\nCartesian conception regarding the mechanism of the universe. There is\nnothing in the physical world but matter and movement.\"\n\nIf we adopt this conception, we are led to construct mechanical\nrepresentations of the material world, and to imagine movements in the\ndifferent parts of bodies capable of reproducing all the\nmanifestations of nature. The kinematic knowledge of these movements,\nthat is to say, the determination of the position, speed, and\nacceleration at a given moment of all the parts of the system, or, on\nthe other hand, their dynamical study, enabling us to know what is the\naction of these parts on each other, would then be sufficient to\nenable us to foretell all that can occur in the domain of nature.\n\nThis was the great thought clearly expressed by the Encyclopaedists of\nthe eighteenth century; and if the necessity of interpreting the\nphenomena of electricity or light led the physicists of last century\nto imagine particular fluids which seemed to obey with some difficulty\nthe ordinary rules of mechanics, these physicists still continued to\nretain their hope in the future, and to treat the idea of Descartes as\nan ideal to be reached sooner or later.\n\nCertain scholars--particularly those of the English School--outrunning\nexperiment, and pushing things to extremes, took pleasure in proposing\nvery curious mechanical models which were often strange images of\nreality. The most illustrious of them, Lord Kelvin, may be considered\nas their representative type, and he has himself said: \"It seems to me\nthat the true sense of the question, Do we or do we not understand a\nparticular subject in physics? is--Can we make a mechanical model\nwhich corresponds to it? I am never satisfied so long as I have been\nunable to make a mechanical model of the object. If I am able to do\nso, I understand it. If I cannot make such a model, I do not\nunderstand it.\" But it must be acknowledged that some of the models\nthus devised have become excessively complicated, and this\ncomplication has for a long time discouraged all but very bold minds.\nIn addition, when it became a question of penetrating into the\nmechanism of molecules, and we were no longer satisfied to look at\nmatter as a mass, the mechanical solutions seemed undetermined and the\nstability of the edifices thus constructed was insufficiently\ndemonstrated.\n\nReturning then to our starting-point, many contemporary physicists\nwish to subject Descartes' idea to strict criticism. From the\nphilosophical point of view, they first enquire whether it is really\ndemonstrated that there exists nothing else in the knowable than\nmatter and movement. They ask themselves whether it is not habit and\ntradition in particular which lead us to ascribe to mechanics the\norigin of phenomena. Perhaps also a question of sense here comes in.\nOur senses, which are, after all, the only windows open towards\nexternal reality, give us a view of one side of the world only;\nevidently we only know the universe by the relations which exist\nbetween it and our organisms, and these organisms are peculiarly\nsensitive to movement.\n\nNothing, however, proves that those acquisitions which are the most\nancient in historical order ought, in the development of science, to\nremain the basis of our knowledge. Nor does any theory prove that our\nperceptions are an exact indication of reality. Many reasons, on the\ncontrary, might be invoked which tend to compel us to see in nature\nphenomena which cannot be reduced to movement.\n\nMechanics as ordinarily understood is the study of reversible\nphenomena. If there be given to the parameter which represents\ntime,[1] and which has assumed increasing values during the duration\nof the phenomena, decreasing values which make it go the opposite way,\nthe whole system will again pass through exactly the same stages as\nbefore, and all the phenomena will unfold themselves in reversed\norder. In physics, the contrary rule appears very general, and\nreversibility generally does not exist. It is an ideal and limited\ncase, which may be sometimes approached, but can never, strictly\nspeaking, be met with in its entirety. No physical phenomenon ever\nrecommences in an identical manner if its direction be altered. It is\ntrue that certain mathematicians warn us that a mechanics can be\ndevised in which reversibility would no longer be the rule, but the\nbold attempts made in this direction are not wholly satisfactory.\n\n[Footnote 1: I.e., the time-curve.--ED.]\n\nOn the other hand, it is established that if a mechanical explanation\nof a phenomenon can be given, we can find an infinity of others which\nlikewise account for all the peculiarities revealed by experiment.\nBut, as a matter of fact, no one has ever succeeded in giving an\nindisputable mechanical representation of the whole physical world.\nEven were we disposed to admit the strangest solutions of the problem;\nto consent, for example, to be satisfied with the hidden systems\ndevised by Helmholtz, whereby we ought to divide variable things into\ntwo classes, some accessible, and the others now and for ever unknown,\nwe should never manage to construct an edifice to contain all the\nknown facts. Even the very comprehensive mechanics of a Hertz fails\nwhere the classical mechanics has not succeeded.\n\nDeeming this check irremediable, many contemporary physicists give up\nattempts which they look upon as condemned beforehand, and adopt, to\nguide them in their researches, a method which at first sight appears\nmuch more modest, and also much more sure. They make up their minds\nnot to see at once to the bottom of things; they no longer seek to\nsuddenly strip the last veils from nature, and to divine her supreme\nsecrets; but they work prudently and advance but slowly, while on the\nground thus conquered foot by foot they endeavour to establish\nthemselves firmly. They study the various magnitudes directly\naccessible to their observation without busying themselves as to their\nessence. They measure quantities of heat and of temperature,\ndifferences of potential, currents, and magnetic fields; and then,\nvarying the conditions, apply the rules of experimental method, and\ndiscover between these magnitudes mutual relations, while they thus\nsucceed in enunciating laws which translate and sum up their labours.\n\nThese empirical laws, however, themselves bring about by induction the\npromulgation of more general laws, which are termed principles. These\nprinciples are originally only the results of experiments, and\nexperiment allows them besides to be checked, and their more or less\nhigh degree of generality to be verified. When they have been thus\ndefinitely established, they may serve as fresh starting-points, and,\nby deduction, lead to very varied discoveries.\n\nThe principles which govern physical science are few in number, and\ntheir very general form gives them a philosophical appearance, while\nwe cannot long resist the temptation of regarding them as metaphysical\ndogmas. It thus happens that the least bold physicists, those who have\nwanted to show themselves the most reserved, are themselves led to\nforget the experimental character of the laws they have propounded,\nand to see in them imperious beings whose authority, placed above all\nverification, can no longer be discussed.\n\nOthers, on the contrary, carry prudence to the extent of timidity.\nThey desire to grievously limit the field of scientific investigation,\nand they assign to science a too restricted domain. They content\nthemselves with representing phenomena by equations, and think that\nthey ought to submit to calculation magnitudes experimentally\ndetermined, without asking themselves whether these calculations\nretain a physical meaning. They are thus led to reconstruct a physics\nin which there again appears the idea of quality, understood, of\ncourse, not in the scholastic sense, since from this quality we can\nargue with some precision by representing it under numerical symbols,\nbut still constituting an element of differentiation and of\nheterogeneity.\n\nNotwithstanding the errors they may lead to if carried to excess, both\nthese doctrines render, as a whole, most important service. It is no\nbad thing that these contradictory tendencies should subsist, for this\nvariety in the conception of phenomena gives to actual science a\ncharacter of intense life and of veritable youth, capable of\nimpassioned efforts towards the truth. Spectators who see such moving\nand varied pictures passing before them, experience the feeling that\nthere no longer exist systems fixed in an immobility which seems that\nof death. They feel that nothing is unchangeable; that ceaseless\ntransformations are taking place before their eyes; and that this\ncontinuous evolution and perpetual change are the necessary conditions\nof progress.\n\nA great number of seekers, moreover, show themselves on their own\naccount perfectly eclectic. They adopt, according to their needs, such\nor such a manner of looking at nature, and do not hesitate to utilize\nvery different images when they appear to them useful and convenient.\nAnd, without doubt, they are not wrong, since these images are only\nsymbols convenient for language. They allow facts to be grouped and\nassociated, but only present a fairly distant resemblance with the\nobjective reality. Hence it is not forbidden to multiply and to modify\nthem according to circumstances. The really essential thing is to\nhave, as a guide through the unknown, a map which certainly does not\nclaim to represent all the aspects of nature, but which, having been\ndrawn up according to predetermined rules, allows us to follow an\nascertained road in the eternal journey towards the truth.\n\nAmong the provisional theories which are thus willingly constructed by\nscholars on their journey, like edifices hastily run up to receive an\nunforeseen harvest, some still appear very bold and very singular.\nAbandoning the search after mechanical models for all electrical\nphenomena, certain physicists reverse, so to speak, the conditions of\nthe problem, and ask themselves whether, instead of giving a\nmechanical interpretation to electricity, they may not, on the\ncontrary, give an electrical interpretation to the phenomena of matter\nand motion, and thus merge mechanics itself in electricity. One thus\nsees dawning afresh the eternal hope of co-ordinating all natural\nphenomena in one grandiose and imposing synthesis. Whatever may be the\nfate reserved for such attempts, they deserve attention in the highest\ndegree; and it is desirable to examine them carefully if we wish to\nhave an exact idea of the tendencies of modern physics.\n\n\n\n\nCHAPTER II\n\nMEASUREMENTS\n\n\nSec. 1. METROLOGY\n\nNot so very long ago, the scholar was often content with qualitative\nobservations. Many phenomena were studied without much trouble being\ntaken to obtain actual measurements. But it is now becoming more and\nmore understood that to establish the relations which exist between\nphysical magnitudes, and to represent the variations of these\nmagnitudes by functions which allow us to use the power of\nmathematical analysis, it is most necessary to express each magnitude\nby a definite number.\n\nUnder these conditions alone can a magnitude be considered as\neffectively known. \"I often say,\" Lord Kelvin has said, \"that if you\ncan measure that of which you are speaking and express it by a number\nyou know something of your subject; but if you cannot measure it nor\nexpress it by a number, your knowledge is of a sorry kind and hardly\nsatisfactory. It may be the beginning of the acquaintance, but you are\nhardly, in your thoughts, advanced towards science, whatever the\nsubject may be.\"\n\nIt has now become possible to measure exactly the elements which enter\ninto nearly all physical phenomena, and these measurements are taken\nwith ever increasing precision. Every time a chapter in science\nprogresses, science shows itself more exacting; it perfects its means\nof investigation, it demands more and more exactitude, and one of the\nmost striking features of modern physics is this constant care for\nstrictness and clearness in experimentation.\n\nA veritable science of measurement has thus been constituted which\nextends over all parts of the domain of physics. This science has its\nrules and its methods; it points out the best processes of\ncalculation, and teaches the method of correctly estimating errors and\ntaking account of them. It has perfected the processes of experiment,\nco-ordinated a large number of results, and made possible the\nunification of standards. It is thanks to it that the system of\nmeasurements unanimously adopted by physicists has been formed.\n\nAt the present day we designate more peculiarly by the name of\nmetrology that part of the science of measurements which devotes\nitself specially to the determining of the prototypes representing the\nfundamental units of dimension and mass, and of the standards of the\nfirst order which are derived from them. If all measurable quantities,\nas was long thought possible, could be reduced to the magnitudes of\nmechanics, metrology would thus be occupied with the essential\nelements entering into all phenomena, and might legitimately claim the\nhighest rank in science. But even when we suppose that some magnitudes\ncan never be connected with mass, length, and time, it still holds a\npreponderating place, and its progress finds an echo throughout the\nwhole domain of the natural sciences. It is therefore well, in order\nto give an account of the general progress of physics, to examine at\nthe outset the improvements which have been effected in these\nfundamental measurements, and to see what precision these improvements\nhave allowed us to attain.\n\n\nSec. 2. THE MEASURE OF LENGTH\n\nTo measure a length is to compare it with another length taken as\nunity. Measurement is therefore a relative operation, and can only\nenable us to know ratios. Did both the length to be measured and the\nunit chosen happen to vary simultaneously and in the same degree, we\nshould perceive no change. Moreover, the unit being, by definition,\nthe term of comparison, and not being itself comparable with anything,\nwe have theoretically no means of ascertaining whether its length\nvaries.\n\nIf, however, we were to note that, suddenly and in the same\nproportions, the distance between two points on this earth had\nincreased, that all the planets had moved further from each other,\nthat all objects around us had become larger, that we ourselves had\nbecome taller, and that the distance travelled by light in the\nduration of a vibration had become greater, we should not hesitate to\nthink ourselves the victims of an illusion, that in reality all these\ndistances had remained fixed, and that all these appearances were due\nto a shortening of the rule which we had used as the standard for\nmeasuring the lengths.\n\nFrom the mathematical point of view, it may be considered that the two\nhypotheses are equivalent; all has lengthened around us, or else our\nstandard has become less. But it is no simple question of convenience\nand simplicity which leads us to reject the one supposition and to\naccept the other; it is right in this case to listen to the voice of\ncommon sense, and those physicists who have an instinctive trust in\nthe notion of an absolute length are perhaps not wrong. It is only by\nchoosing our unit from those which at all times have seemed to all men\nthe most invariable, that we are able in our experiments to note that\nthe same causes acting under identical conditions always produce the\nsame effects. The idea of absolute length is derived from the\nprinciple of causality; and our choice is forced upon us by the\nnecessity of obeying this principle, which we cannot reject without\ndeclaring by that very act all science to be impossible.\n\nSimilar remarks might be made with regard to the notions of absolute\ntime and absolute movement. They have been put in evidence and set\nforth very forcibly by a learned and profound mathematician, M.\nPainleve.\n\nOn the particularly clear example of the measure of length, it is\ninteresting to follow the evolution of the methods employed, and to\nrun through the history of the progress in precision from the time\nthat we have possessed authentic documents relating to this question.\nThis history has been written in a masterly way by one of the\nphysicists who have in our days done the most by their personal\nlabours to add to it glorious pages. M. Benoit, the learned Director\nof the International Bureau of Weights and Measures, has furnished in\nvarious reports very complete details on the subject, from which I\nhere borrow the most interesting.\n\nWe know that in France the fundamental standard for measures of length\nwas for a long time the _Toise du Chatelet_, a kind of callipers\nformed of a bar of iron which in 1668 was embedded in the outside wall\nof the Chatelet, at the foot of the staircase. This bar had at its\nextremities two projections with square faces, and all the _toises_ of\ncommerce had to fit exactly between them. Such a standard, roughly\nconstructed, and exposed to all the injuries of weather and time,\noffered very slight guarantees either as to the permanence or the\ncorrectness of its copies. Nothing, perhaps, can better convey an idea\nof the importance of the modifications made in the methods of\nexperimental physics than the easy comparison between so rudimentary a\nprocess and the actual measurements effected at the present time.\n\nThe _Toise du Chatelet_, notwithstanding its evident faults, was\nemployed for nearly a hundred years; in 1766 it was replaced by the\n_Toise du Perou_, so called because it had served for the measurements\nof the terrestrial arc effected in Peru from 1735 to 1739 by Bouguer,\nLa Condamine, and Godin. At that time, according to the comparisons\nmade between this new _toise_ and the _Toise du Nord_, which had also\nbeen used for the measurement of an arc of the meridian, an error of\nthe tenth part of a millimetre in measuring lengths of the order of a\nmetre was considered quite unimportant. At the end of the eighteenth\ncentury, Delambre, in his work _Sur la Base du Systeme metrique\ndecimal_, clearly gives us to understand that magnitudes of the order\nof the hundredth of a millimetre appear to him incapable of\nobservation, even in scientific researches of the highest precision.\nAt the present date the International Bureau of Weights and Measures\nguarantees, in the determination of a standard of length compared with\nthe metre, an approximation of two or three ten-thousandths of a\nmillimetre, and even a little more under certain circumstances.\n\nThis very remarkable progress is due to the improvements in the method\nof comparison on the one hand, and in the manufacture of the standard\non the other. M. Benoit rightly points out that a kind of competition\nhas been set up between the standard destined to represent the unit\nwith its subdivisions and multiples and the instrument charged with\nobserving it, comparable, up to a certain point, with that which in\nanother order of ideas goes on between the gun and the armour-plate.\n\nThe measuring instrument of to-day is an instrument of comparison\nconstructed with meticulous care, which enables us to do away with\ncauses of error formerly ignored, to eliminate the action of external\nphenomena, and to withdraw the experiment from the influence of even\nthe personality of the observer. This standard is no longer, as\nformerly, a flat rule, weak and fragile, but a rigid bar, incapable of\ndeformation, in which the material is utilised in the best conditions\nof resistance. For a standard with ends has been substituted a\nstandard with marks, which permits much more precise definition and\ncan be employed in optical processes of observation alone; that is, in\nprocesses which can produce in it no deformation and no alteration.\nMoreover, the marks are traced on the plane of the neutral fibres[2]\nexposed, and the invariability of their distance apart is thus\nassured, even when a change is made in the way the rule is supported.\n\n[Footnote 2: The author seems to refer to the fact that in the\nstandard metre, the measurement is taken from the central one of three\nmarks at each end of the bar. The transverse section of the bar is an\nX, and the reading is made by a microscope.--ED.]\n\nThanks to studies thus systematically pursued, we have succeeded in\nthe course of a hundred years in increasing the precision of measures\nin the proportion of a thousand to one, and we may ask ourselves\nwhether such an increase will continue in the future. No doubt\nprogress will not be stayed; but if we keep to the definition of\nlength by a material standard, it would seem that its precision cannot\nbe considerably increased. We have nearly reached the limit imposed by\nthe necessity of making strokes of such a thickness as to be\nobservable under the microscope.\n\nIt may happen, however, that we shall be brought one of these days to\na new conception of the measure of length, and that very different\nprocesses of determination will be thought of. If we took as unit, for\ninstance, the distance covered by a given radiation during a\nvibration, the optical processes would at once admit of much greater\nprecision.\n\nThus Fizeau, the first to have this idea, says: \"A ray of light, with\nits series of undulations of extreme tenuity but perfect regularity,\nmay be considered as a micrometer of the greatest perfection, and\nparticularly suitable for determining length.\" But in the present\nstate of things, since the legal and customary definition of the unit\nremains a material standard, it is not enough to measure length in\nterms of wave-lengths, and we must also know the value of these\nwave-lengths in terms of the standard prototype of the metre.\n\nThis was determined in 1894 by M. Michelson and M. Benoit in an\nexperiment which will remain classic. The two physicists measured a\nstandard length of about ten centimetres, first in terms of the\nwave-lengths of the red, green, and blue radiations of cadmium, and\nthen in terms of the standard metre. The great difficulty of the\nexperiment proceeds from the vast difference which exists between the\nlengths to be compared, the wave-lengths barely amounting to half a\nmicron;[3] the process employed consisted in noting, instead of this\nlength, a length easily made about a thousand times greater, namely,\nthe distance between the fringes of interference.\n\n[Footnote 3: I.e. 1/2000 of a millimetre.--ED.]\n\nIn all measurement, that is to say in every determination of the\nrelation of a magnitude to the unit, there has to be determined on the\none hand the whole, and on the other the fractional part of this\nratio, and naturally the most delicate determination is generally that\nof this fractional part. In optical processes the difficulty is\nreversed. The fractional part is easily known, while it is the high\nfigure of the number representing the whole which becomes a very\nserious obstacle. It is this obstacle which MM. Michelson and Benoit\novercame with admirable ingenuity. By making use of a somewhat similar\nidea, M. Mace de Lepinay and MM. Perot and Fabry, have lately effected\nby optical methods, measurements of the greatest precision, and no\ndoubt further progress may still be made. A day may perhaps come when\na material standard will be given up, and it may perhaps even be\nrecognised that such a standard in time changes its length by\nmolecular strain, and by wear and tear: and it will be further noted\nthat, in accordance with certain theories which will be noticed later\non, it is not invariable when its orientation is changed.\n\nFor the moment, however, the need of any change in the definition of\nthe unit is in no way felt; we must, on the contrary, hope that the\nuse of the unit adopted by the physicists of the whole world will\nspread more and more. It is right to remark that a few errors still\noccur with regard to this unit, and that these errors have been\nfacilitated by incoherent legislation. France herself, though she was\nthe admirable initiator of the metrical system, has for too long\nallowed a very regrettable confusion to exist; and it cannot be noted\nwithout a certain sadness that it was not until the _11th July 1903_\nthat a law was promulgated re-establishing the agreement between the\nlegal and the scientific definition of the metre.\n\nPerhaps it may not be useless to briefly indicate here the reasons of\nthe disagreement which had taken place. Two definitions of the metre\ncan be, and in fact were given. One had for its basis the dimensions\nof the earth, the other the length of the material standard. In the\nminds of the founders of the metrical system, the first of these was\nthe true definition of the unit of length, the second merely a simple\nrepresentation. It was admitted, however, that this representation had\nbeen constructed in a manner perfect enough for it to be nearly\nimpossible to perceive any difference between the unit and its\nrepresentation, and for the practical identity of the two definitions\nto be thus assured. The creators of the metrical system were persuaded\nthat the measurements of the meridian effected in their day could\nnever be surpassed in precision; and on the other hand, by borrowing\nfrom nature a definite basis, they thought to take from the definition\nof the unit some of its arbitrary character, and to ensure the means\nof again finding the same unit if by any accident the standard became\naltered. Their confidence in the value of the processes they had seen\nemployed was exaggerated, and their mistrust of the future\nunjustified. This example shows how imprudent it is to endeavour to\nfix limits to progress. It is an error to think the march of science\ncan be stayed; and in reality it is now known that the ten-millionth\npart of the quarter of the terrestrial meridian is longer than the\nmetre by 0.187 millimetres. But contemporary physicists do not fall\ninto the same error as their forerunners, and they regard the present\nresult as merely provisional. They guess, in fact, that new\nimprovements will be effected in the art of measurement; they know\nthat geodesical processes, though much improved in our days, have\nstill much to do to attain the precision displayed in the construction\nand determination of standards of the first order; and consequently\nthey do not propose to keep the ancient definition, which would lead\nto having for unit a magnitude possessing the grave defect from a\npractical point of view of being constantly variable.\n\nWe may even consider that, looked at theoretically, its permanence\nwould not be assured. Nothing, in fact, proves that sensible\nvariations may not in time be produced in the value of an arc of the\nmeridian, and serious difficulties may arise regarding the probable\ninequality of the various meridians.\n\nFor all these reasons, the idea of finding a natural unit has been\ngradually abandoned, and we have become resigned to accepting as a\nfundamental unit an arbitrary and conventional length having a\nmaterial representation recognised by universal consent; and it was\nthis unit which was consecrated by the following law of the 11th July\n1903:--\n\n\"The standard prototype of the metrical system is the international\nmetre, which has been sanctioned by the General Conference on Weights\nand Measures.\"\n\n\nSec. 3. THE MEASURE OF MASS\n\nOn the subject of measures of mass, similar remarks to those on\nmeasures of length might be made. The confusion here was perhaps still\ngreater, because, to the uncertainty relating to the fixing of the\nunit, was added some indecision on the very nature of the magnitude\ndefined. In law, as in ordinary practice, the notions of weight and of\nmass were not, in fact, separated with sufficient clearness.\n\nThey represent, however, two essentially different things. Mass is the\ncharacteristic of a quantity of matter; it depends neither on the\ngeographical position one occupies nor on the altitude to which one\nmay rise; it remains invariable so long as nothing material is added\nor taken away. Weight is the action which gravity has upon the body\nunder consideration; this action does not depend solely on the body,\nbut on the earth as well; and when it is changed from one spot to\nanother, the weight changes, because gravity varies with latitude and\naltitude.\n\nThese elementary notions, to-day understood even by young beginners,\nappear to have been for a long time indistinctly grasped. The\ndistinction remained confused in many minds, because, for the most\npart, masses were comparatively estimated by the intermediary of\nweights. The estimations of weight made with the balance utilize the\naction of the weight on the beam, but in such conditions that the\ninfluence of the variations of gravity becomes eliminated. The two\nweights which are being compared may both of them change if the\nweighing is effected in different places, but they are attracted in\nthe same proportion. If once equal, they remain equal even when in\nreality they may both have varied.\n\nThe current law defines the kilogramme as the standard of mass, and\nthe law is certainly in conformity with the rather obscurely expressed\nintentions of the founders of the metrical system. Their terminology\nwas vague, but they certainly had in view the supply of a standard for\ncommercial transactions, and it is quite evident that in barter what\nis important to the buyer as well as to the seller is not the\nattraction the earth may exercise on the goods, but the quantity that\nmay be supplied for a given price. Besides, the fact that the founders\nabstained from indicating any specified spot in the definition of the\nkilogramme, when they were perfectly acquainted with the considerable\nvariations in the intensity of gravity, leaves no doubt as to their\nreal desire.\n\nThe same objections have been made to the definition of the\nkilogramme, at first considered as the mass of a cubic decimetre of\nwater at 4 deg. C., as to the first definition of the metre. We must\nadmire the incredible precision attained at the outset by the\nphysicists who made the initial determinations, but we know at the\npresent day that the kilogramme they constructed is slightly too heavy\n(by about 1/25,000). Very remarkable researches have been carried out\nwith regard to this determination by the International Bureau, and by\nMM. Mace de Lepinay and Buisson. The law of the 11th July 1903 has\ndefinitely regularized the custom which physicists had adopted some\nyears before; and the standard of mass, the legal prototype of the\nmetrical system, is now the international kilogramme sanctioned by the\nConference of Weights and Measures.\n\nThe comparison of a mass with the standard is effected with a\nprecision to which no other measurement can attain. Metrology vouches\nfor the hundredth of a milligramme in a kilogramme; that is to say,\nthat it estimates the hundred-millionth part of the magnitude studied.\n\nWe may--as in the case of the lengths--ask ourselves whether this\nalready admirable precision can be surpassed; and progress would seem\nlikely to be slow, for difficulties singularly increase when we get to\nsuch small quantities. But it is permitted to hope that the physicists\nof the future will do still better than those of to-day; and perhaps\nwe may catch a glimpse of the time when we shall begin to observe that\nthe standard, which is constructed from a heavy metal, namely,\niridium-platinum, itself obeys an apparently general law, and little\nby little loses some particles of its mass by emanation.\n\n\nSec. 4. THE MEASURE OF TIME\n\nThe third fundamental magnitude of mechanics is time. There is, so to\nspeak, no physical phenomenon in which the notion of time linked to\nthe sequence of our states of consciousness does not play a\nconsiderable part.\n\nAncestral habits and a very early tradition have led us to preserve,\nas the unit of time, a unit connected with the earth's movement; and\nthe unit to-day adopted is, as we know, the sexagesimal second of mean\ntime. This magnitude, thus defined by the conditions of a natural\nmotion which may itself be modified, does not seem to offer all the\nguarantees desirable from the point of view of invariability. It is\ncertain that all the friction exercised on the earth--by the tides,\nfor instance--must slowly lengthen the duration of the day, and must\ninfluence the movement of the earth round the sun. Such influence is\ncertainly very slight, but it nevertheless gives an unfortunately\narbitrary character to the unit adopted.\n\nWe might have taken as the standard of time the duration of another\nnatural phenomenon, which appears to be always reproduced under\nidentical conditions; the duration, for instance, of a given luminous\nvibration. But the experimental difficulties of evaluation with such a\nunit of the times which ordinarily have to be considered, would be so\ngreat that such a reform in practice cannot be hoped for. It should,\nmoreover, be remarked that the duration of a vibration may itself be\ninfluenced by external circumstances, among which are the variations\nof the magnetic field in which its source is placed. It could not,\ntherefore, be strictly considered as independent of the earth; and the\ntheoretical advantage which might be expected from this alteration\nwould be somewhat illusory.\n\nPerhaps in the future recourse may be had to very different phenomena.\nThus Curie pointed out that if the air inside a glass tube has been\nrendered radioactive by a solution of radium, the tube may be sealed\nup, and it will then be noted that the radiation of its walls\ndiminishes with time, in accordance with an exponential law. The\nconstant of time derived by this phenomenon remains the same whatever\nthe nature and dimensions of the walls of the tube or the temperature\nmay be, and time might thus be denned independently of all the other\nunits.\n\nWe might also, as M. Lippmann has suggested in an extremely ingenious\nway, decide to obtain measures of time which can be considered as\nabsolute because they are determined by parameters of another nature\nthan that of the magnitude to be measured. Such experiments are made\npossible by the phenomena of gravitation. We could employ, for\ninstance, the pendulum by adopting, as the unit of force, the force\nwhich renders the constant of gravitation equal to unity. The unit of\ntime thus defined would be independent of the unit of length, and\nwould depend only on the substance which would give us the unit of\nmass under the unit of volume.\n\nIt would be equally possible to utilize electrical phenomena, and one\nmight devise experiments perfectly easy of execution. Thus, by\ncharging a condenser by means of a battery, and discharging it a given\nnumber of times in a given interval of time, so that the effect of the\ncurrent of discharge should be the same as the effect of the output of\nthe battery through a given resistance, we could estimate, by the\nmeasurement of the electrical magnitudes, the duration of the interval\nnoted. A system of this kind must not be looked upon as a simple _jeu\nd'esprit_, since this very practicable experiment would easily permit\nus to check, with a precision which could be carried very far, the\nconstancy of an interval of time.\n\nFrom the practical point of view, chronometry has made in these last\nfew years very sensible progress. The errors in the movements of\nchronometers are corrected in a much more systematic way than\nformerly, and certain inventions have enabled important improvements\nto be effected in the construction of these instruments. Thus the\ncurious properties which steel combined with nickel--so admirably\nstudied by M.Ch.Ed. Guillaume--exhibits in the matter of dilatation\nare now utilized so as to almost completely annihilate the influence\nof variations of temperature.\n\n\nSec. 5. THE MEASURE OF TEMPERATURE\n\nFrom the three mechanical units we derive secondary units; as, for\ninstance, the unit of work or mechanical energy. The kinetic theory\ntakes temperature, as well as heat itself, to be a quantity of energy,\nand thus seems to connect this notion with the magnitudes of\nmechanics. But the legitimacy of this theory cannot be admitted, and\nthe calorific movement should also be a phenomenon so strictly\nconfined in space that our most delicate means of investigation would\nnot enable us to perceive it. It is better, then, to continue to\nregard the unit of difference of temperature as a distinct unit, to be\nadded to the fundamental units.\n\nTo define the measure of a certain temperature, we take, in practice,\nsome arbitrary property of a body. The only necessary condition of\nthis property is, that it should constantly vary in the same direction\nwhen the temperature rises, and that it should possess, at any\ntemperature, a well-marked value. We measure this value by melting ice\nand by the vapour of boiling water under normal pressure, and the\nsuccessive hundredths of its variation, beginning with the melting\nice, defines the percentage. Thermodynamics, however, has made it\nplain that we can set up a thermometric scale without relying upon any\ndetermined property of a real body. Such a scale has an absolute value\nindependently of the properties of matter. Now it happens that if we\nmake use for the estimation of temperatures, of the phenomena of\ndilatation under a constant pressure, or of the increase of pressure\nin a constant volume of a gaseous body, we obtain a scale very near\nthe absolute, which almost coincides with it when the gas possesses\ncertain qualities which make it nearly what is called a perfect gas.\nThis most lucky coincidence has decided the choice of the convention\nadopted by physicists. They define normal temperature by means of the\nvariations of pressure in a mass of hydrogen beginning with the\ninitial pressure of a metre of mercury at 0 deg. C.\n\nM.P. Chappuis, in some very precise experiments conducted with much\nmethod, has proved that at ordinary temperatures the indications of\nsuch a thermometer are so close to the degrees of the theoretical\nscale that it is almost impossible to ascertain the value of the\ndivergences, or even the direction that they take. The divergence\nbecomes, however, manifest when we work with extreme temperatures. It\nresults from the useful researches of M. Daniel Berthelot that we must\nsubtract +0.18 deg. from the indications of the hydrogen thermometer\ntowards the temperature -240 deg. C, and add +0.05 deg. to 1000 deg.\nto equate them with the thermodynamic scale. Of course, the difference\nwould also become still more noticeable on getting nearer to the\nabsolute zero; for as hydrogen gets more and more cooled, it gradually\nexhibits in a lesser degree the characteristics of a perfect gas.\n\nTo study the lower regions which border on that kind of pole of cold\ntowards which are straining the efforts of the many physicists who\nhave of late years succeeded in getting a few degrees further forward,\nwe may turn to a gas still more difficult to liquefy than hydrogen.\nThus, thermometers have been made of helium; and from the temperature\nof -260 deg. C. downward the divergence of such a thermometer from one of\nhydrogen is very marked.\n\nThe measurement of very high temperatures is not open to the same\ntheoretical objections as that of very low temperatures; but, from a\npractical point of view, it is as difficult to effect with an ordinary\ngas thermometer. It becomes impossible to guarantee the reservoir\nremaining sufficiently impermeable, and all security disappears,\nnotwithstanding the use of recipients very superior to those of former\ntimes, such as those lately devised by the physicists of the\n_Reichansalt_. This difficulty is obviated by using other methods,\nsuch as the employment of thermo-electric couples, such as the very\nconvenient couple of M. le Chatelier; but the graduation of these\ninstruments can only be effected at the cost of a rather bold\nextrapolation.\n\nM.D. Berthelot has pointed out and experimented with a very\ninteresting process, founded on the measurement by the phenomena of\ninterference of the refractive index of a column of air subjected to\nthe temperature it is desired to measure. It appears admissible that\neven at the highest temperatures the variation of the power of\nrefraction is strictly proportional to that of the density, for this\nproportion is exactly verified so long as it is possible to check it\nprecisely. We can thus, by a method which offers the great advantage\nof being independent of the power and dimension of the envelopes\nemployed--since the length of the column of air considered alone\nenters into the calculation--obtain results equivalent to those given\nby the ordinary air thermometer.\n\nAnother method, very old in principle, has also lately acquired great\nimportance. For a long time we sought to estimate the temperature of a\nbody by studying its radiation, but we did not know any positive\nrelation between this radiation and the temperature, and we had no\ngood experimental method of estimation, but had recourse to purely\nempirical formulas and the use of apparatus of little precision. Now,\nhowever, many physicists, continuing the classic researches of\nKirchhoff, Boltzmann, Professors Wien and Planck, and taking their\nstarting-point from the laws of thermodynamics, have given formulas\nwhich establish the radiating power of a dark body as a function of\nthe temperature and the wave-length, or, better still, of the total\npower as a function of the temperature and wave-length corresponding\nto the maximum value of the power of radiation. We see, therefore, the\npossibility of appealing for the measurement of temperature to a\nphenomenon which is no longer the variation of the elastic force of a\ngas, and yet is also connected with the principles of thermodynamics.\n\nThis is what Professors Lummer and Pringsheim have shown in a series\nof studies which may certainly be reckoned among the greatest\nexperimental researches of the last few years. They have constructed a\nradiator closely resembling the theoretically integral radiator which\na closed isothermal vessel would be, and with only a very small\nopening, which allows us to collect from outside the radiations which\nare in equilibrium with the interior. This vessel is formed of a\nhollow carbon cylinder, heated by a current of high intensity; the\nradiations are studied by means of a bolometer, the disposition of\nwhich varies with the nature of the experiments.\n\nIt is hardly possible to enter into the details of the method, but the\nresult sufficiently indicates its importance. It is now possible,\nthanks to their researches, to estimate a temperature of 2000 deg. C. to\nwithin about 5 deg. Ten years ago a similar approximation could hardly\nhave been arrived at for a temperature of 1000 deg. C.\n\n\nSec. 6. DERIVED UNITS AND THE MEASURE OF A QUANTITY OF ENERGY\n\nIt must be understood that it is only by arbitrary convention that a\ndependency is established between a derived unit and the fundamental\nunits. The laws of numbers in physics are often only laws of\nproportion. We transform them into laws of equation, because we\nintroduce numerical coefficients and choose the units on which they\ndepend so as to simplify as much as possible the formulas most in use.\nA particular speed, for instance, is in reality nothing else but a\nspeed, and it is only by the peculiar choice of unit that we can say\nthat it is the space covered during the unit of time. In the same way,\na quantity of electricity is a quantity of electricity; and there is\nnothing to prove that, in its essence, it is really reducible to a\nfunction of mass, of length, and of time.\n\nPersons are still to be met with who seem to have some illusions on\nthis point, and who see in the doctrine of the dimensions of the units\na doctrine of general physics, while it is, to say truth, only a\ndoctrine of metrology. The knowledge of dimensions is valuable, since\nit allows us, for instance, to easily verify the homogeneity of a\nformula, but it can in no way give us any information on the actual\nnature of the quantity measured.\n\nMagnitudes to which we attribute like dimensions may be qualitatively\nirreducible one to the other. Thus the different forms of energy are\nmeasured by the same unit, and yet it seems that some of them, such as\nkinetic energy, really depend on time; while for others, such as\npotential energy, the dependency established by the system of\nmeasurement seems somewhat fictitious.\n\nThe numerical value of a quantity of energy of any nature should, in\nthe system C.G.S., be expressed in terms of the unit called the erg;\nbut, as a matter of fact, when we wish to compare and measure\ndifferent quantities of energy of varying forms, such as electrical,\nchemical, and other quantities, etc., we nearly always employ a method\nby which all these energies are finally transformed and used to heat\nthe water of a calorimeter. It is therefore very important to study\nwell the calorific phenomenon chosen as the unit of heat, and to\ndetermine with precision its mechanical equivalent, that is to say,\nthe number of ergs necessary to produce this unit. This is a number\nwhich, on the principle of equivalence, depends neither on the method\nemployed, nor the time, nor any other external circumstance.\n\nAs the result of the brilliant researches of Rowland and of Mr\nGriffiths on the variations of the specific heat of water, physicists\nhave decided to take as calorific standard the quantity of heat\nnecessary to raise a gramme of water from 15 deg. to 16 deg. C., the\ntemperature being measured by the scale of the hydrogen thermometer of\nthe International Bureau.\n\nOn the other hand, new determinations of the mechanical equivalent,\namong which it is right to mention that of Mr. Ames, and a full\ndiscussion as to the best results, have led to the adoption of the\nnumber 4.187 to represent the number of ergs capable of producing the\nunit of heat.\n\nIn practice, the measurement of a quantity of heat is very often\neffected by means of the ice calorimeter, the use of which is\nparticularly simple and convenient. There is, therefore, a very\nspecial interest in knowing exactly the melting-point of ice. M.\nLeduc, who for several years has measured a great number of physical\nconstants with minute precautions and a remarkable sense of precision,\nconcludes, after a close discussion of the various results obtained,\nthat this heat is equal to 79.1 calories. An error of almost a calorie\nhad been committed by several renowned experimenters, and it will be\nseen that in certain points the art of measurement may still be\nlargely perfected.\n\nTo the unit of energy might be immediately attached other units. For\ninstance, radiation being nothing but a flux of energy, we could, in\norder to establish photometric units, divide the normal spectrum into\nbands of a given width, and measure the power of each for the unit of\nradiating surface.\n\nBut, notwithstanding some recent researches on this question, we\ncannot yet consider the distribution of energy in the spectrum as\nperfectly known. If we adopt the excellent habit which exists in some\nresearches of expressing radiating energy in ergs, it is still\ncustomary to bring the radiations to a standard giving, by its\nconstitution alone, the unit of one particular radiation. In\nparticular, the definitions are still adhered to which were adopted as\nthe result of the researches of M. Violle on the radiation of fused\nplatinum at the temperature of solidification; and most physicists\nutilize in the ordinary methods of photometry the clearly defined\nnotions of M. Blondel as to the luminous intensity of flux,\nillumination (_eclairement_), light (_eclat_), and lighting\n(_eclairage_), with the corresponding units, decimal candle, _lumen_,\n_lux_, carcel lamp, candle per square centimetre, and _lumen_-hour.[4]\n\n[Footnote 4: These are the magnitudes and units adopted at the\nInternational Congress of Electricians in 1904. For their definition\nand explanation, see Demanet, _Notes de Physique Experimentale_\n(Louvain, 1905), t. iv. p. 8.--ED.]\n\n\nSec. 7. MEASURE OF CERTAIN PHYSICAL CONSTANTS\n\nThe progress of metrology has led, as a consequence, to corresponding\nprogress in nearly all physical measurements, and particularly in the\nmeasure of natural constants. Among these, the constant of gravitation\noccupies a position quite apart from the importance and simplicity of\nthe physical law which defines it, as well as by its generality. Two\nmaterial particles are mutually attracted to each other by a force\ndirectly proportional to the product of their mass, and inversely\nproportional to the square of the distance between them. The\ncoefficient of proportion is determined when once the units are\nchosen, and as soon as we know the numerical values of this force, of\nthe two masses, and of their distance. But when we wish to make\nlaboratory experiments serious difficulties appear, owing to the\nweakness of the attraction between masses of ordinary dimensions.\nMicroscopic forces, so to speak, have to be observed, and therefore\nall the causes of errors have to be avoided which would be unimportant\nin most other physical researches. It is known that Cavendish was the\nfirst who succeeded by means of the torsion balance in effecting\nfairly precise measurements. This method has been again taken in hand\nby different experimenters, and the most recent results are due to Mr\nVernon Boys. This learned physicist is also the author of a most\nuseful practical invention, and has succeeded in making quartz threads\nas fine as can be desired and extremely uniform. He finds that these\nthreads possess valuable properties, such as perfect elasticity and\ngreat tenacity. He has been able, with threads not more than 1/500 of\na millimetre in diameter, to measure with precision couples of an\norder formerly considered outside the range of experiment, and to\nreduce the dimensions of the apparatus of Cavendish in the proportion\nof 150 to 1. The great advantage found in the use of these small\ninstruments is the better avoidance of the perturbations arising from\ndraughts of air, and of the very serious influence of the slightest\ninequality in temperature.\n\nOther methods have been employed in late years by other experimenters,\nsuch as the method of Baron Eoetvoes, founded on the use of a torsion\nlever, the method of the ordinary balance, used especially by\nProfessors Richarz and Krigar-Menzel and also by Professor Poynting,\nand the method of M. Wilsing, who uses a balance with a vertical beam.\nThe results fairly agree, and lead to attributing to the earth a\ndensity equal to 5.527.\n\nThe most familiar manifestation of gravitation is gravity. The action\nof the earth on the unit of mass placed in one point, and the\nintensity of gravity, is measured, as we know, by the aid of a\npendulum. The methods of measurement, whether by absolute or by\nrelative determinations, so greatly improved by Borda and Bessel, have\nbeen still further improved by various geodesians, among whom should\nbe mentioned M. von Sterneek and General Defforges. Numerous\nobservations have been made in all parts of the world by various\nexplorers, and have led to a fairly complete knowledge of the\ndistribution of gravity over the surface of the globe. Thus we have\nsucceeded in making evident anomalies which would not easily find\ntheir place in the formula of Clairaut.\n\nAnother constant, the determination of which is of the greatest\nutility in astronomy of position, and the value of which enters into\nelectromagnetic theory, has to-day assumed, with the new ideas on the\nconstitution of matter, a still more considerable importance. I refer\nto the speed of light, which appears to us, as we shall see further\non, the maximum value of speed which can be given to a material body.\n\nAfter the historical experiments of Fizeau and Foucault, taken up\nafresh, as we know, partly by Cornu, and partly by Michelson and\nNewcomb, it remained still possible to increase the precision of the\nmeasurements. Professor Michelson has undertaken some new researches\nby a method which is a combination of the principle of the toothed\nwheel of Fizeau with the revolving mirror of Foucault. The toothed\nwheel is here replaced, however, by a grating, in which the lines and\nthe spaces between them take the place of the teeth and the gaps, the\nreflected light only being returned when it strikes on the space\nbetween two lines. The illustrious American physicist estimates that\nhe can thus evaluate to nearly five kilometres the path traversed by\nlight in one second. This approximation corresponds to a relative\nvalue of a few hundred-thousandths, and it far exceeds those hitherto\nattained by the best experimenters. When all the experiments are\ncompleted, they will perhaps solve certain questions still in\nsuspense; for instance, the question whether the speed of propagation\ndepends on intensity. If this turns out to be the case, we should be\nbrought to the important conclusion that the amplitude of the\noscillations, which is certainly very small in relation to the already\ntiny wave-lengths, cannot be considered as unimportant in regard to\nthese lengths. Such would seem to have been the result of the curious\nexperiments of M. Muller and of M. Ebert, but these results have been\nrecently disputed by M. Doubt.\n\nIn the case of sound vibrations, on the other hand, it should be noted\nthat experiment, consistently with the theory, proves that the speed\nincreases with the amplitude, or, if you will, with the intensity. M.\nViolle has published an important series of experiments on the speed\nof propagation of very condensed waves, on the deformations of these\nwaves, and on the relations of the speed and the pressure, which\nverify in a remarkable manner the results foreshadowed by the already\nold calculations of Riemann, repeated later by Hugoniot. If, on the\ncontrary, the amplitude is sufficiently small, there exists a speed\nlimit which is the same in a large pipe and in free air. By some\nbeautiful experiments, MM. Violle and Vautier have clearly shown that\nany disturbance in the air melts somewhat quickly into a single wave\nof given form, which is propagated to a distance, while gradually\nbecoming weaker and showing a constant speed which differs little in\ndry air at 0 deg. C. from 331.36 metres per second. In a narrow pipe the\ninfluence of the walls makes itself felt and produces various effects,\nin particular a kind of dispersion in space of the harmonics of the\nsound. This phenomenon, according to M. Brillouin, is perfectly\nexplicable by a theory similar to the theory of gratings.\n\n\n\n\nCHAPTER III\n\nPRINCIPLES\n\n\nSec. 1. THE PRINCIPLES OF PHYSICS\n\nFacts conscientiously observed lead by induction to the enunciation of\na certain number of laws or general hypotheses which are the\nprinciples already referred to. These principal hypotheses are, in the\neyes of a physicist, legitimate generalizations, the consequences of\nwhich we shall be able at once to check by the experiments from which\nthey issue.\n\nAmong the principles almost universally adopted until lately figure\nprominently those of mechanics--such as the principle of relativity,\nand the principle of the equality of action and reaction. We will not\ndetail nor discuss them here, but later on we shall have an\nopportunity of pointing out how recent theories on the phenomena of\nelectricity have shaken the confidence of physicists in them and have\nled certain scholars to doubt their absolute value.\n\nThe principle of Lavoisier, or principle of the conservation of mass,\npresents itself under two different aspects according to whether mass\nis looked upon as the coefficient of the inertia of matter or as the\nfactor which intervenes in the phenomena of universal attraction, and\nparticularly in gravitation. We shall see when we treat of these\ntheories, how we have been led to suppose that inertia depended on\nvelocity and even on direction. If this conception were exact, the\nprinciple of the invariability of mass would naturally be destroyed.\nConsidered as a factor of attraction, is mass really indestructible?\n\nA few years ago such a question would have seemed singularly\naudacious. And yet the law of Lavoisier is so far from self-evident\nthat for centuries it escaped the notice of physicists and chemists.\nBut its great apparent simplicity and its high character of\ngenerality, when enunciated at the end of the eighteenth century,\nrapidly gave it such an authority that no one was able to any longer\ndispute it unless he desired the reputation of an oddity inclined to\nparadoxical ideas.\n\nIt is important, however, to remark that, under fallacious\nmetaphysical appearances, we are in reality using empty words\nwhen we repeat the aphorism, \"Nothing can be lost, nothing can be\ncreated,\" and deduce from it the indestructibility of matter. This\nindestructibility, in truth, is an experimental fact, and the\nprinciple depends on experiment. It may even seem, at first sight,\nmore singular than not that the weight of a bodily system in a given\nplace, or the quotient of this weight by that of the standard\nmass--that is to say, the mass of these bodies--remains invariable,\nboth when the temperature changes and when chemical reagents cause the\noriginal materials to disappear and to be replaced by new ones. We may\ncertainly consider that in a chemical phenomenon annihilations and\ncreations of matter are really produced; but the experimental law\nteaches us that there is compensation in certain respects.\n\nThe discovery of the radioactive bodies has, in some sort, rendered\npopular the speculations of physicists on the phenomena of the\ndisaggregation of matter. We shall have to seek the exact meaning\nwhich ought to be given to the experiments on the emanation of these\nbodies, and to discover whether these experiments really imperil the\nlaw of Lavoisier.\n\nFor some years different experimenters have also effected many very\nprecise measurements of the weight of divers bodies both before and\nafter chemical reactions between these bodies. Two highly experienced\nand cautious physicists, Professors Landolt and Heydweiller, have not\nhesitated to announce the sensational result that in certain\ncircumstances the weight is no longer the same after as before the\nreaction. In particular, the weight of a solution of salts of copper\nin water is not the exact sum of the joint weights of the salt and the\nwater. Such experiments are evidently very delicate; they have been\ndisputed, and they cannot be considered as sufficient for conviction.\nIt follows nevertheless that it is no longer forbidden to regard the\nlaw of Lavoisier as only an approximate law; according to Sandford and\nRay, this approximation would be about 1/2,400,000. This is also the\nresult reached by Professor Poynting in experiments regarding the\npossible action of temperature on the weight of a body; and if this be\nreally so, we may reassure ourselves, and from the point of view of\npractical application may continue to look upon matter as\nindestructible.\n\nThe principles of physics, by imposing certain conditions on\nphenomena, limit after a fashion the field of the possible. Among\nthese principles is one which, notwithstanding its importance when\ncompared with that of universally known principles, is less familiar\nto some people. This is the principle of symmetry, more or less\nconscious applications of which can, no doubt, be found in various\nworks and even in the conceptions of Copernican astronomers, but which\nwas generalized and clearly enunciated for the first time by the late\nM. Curie. This illustrious physicist pointed out the advantage of\nintroducing into the study of physical phenomena the considerations on\nsymmetry familiar to crystallographers; for a phenomenon to take\nplace, it is necessary that a certain dissymmetry should previously\nexist in the medium in which this phenomenon occurs. A body, for\ninstance, may be animated with a certain linear velocity or a speed of\nrotation; it may be compressed, or twisted; it may be placed in an\nelectric or in a magnetic field; it may be affected by an electric\ncurrent or by one of heat; it may be traversed by a ray of light\neither ordinary or polarized rectilineally or circularly, etc.:--in\neach case a certain minimum and characteristic dissymmetry is\nnecessary at every point of the body in question.\n\nThis consideration enables us to foresee that certain phenomena which\nmight be imagined _a priori_ cannot exist. Thus, for instance, it is\nimpossible that an electric field, a magnitude directed and not\nsuperposable on its image in a mirror perpendicular to its direction,\ncould be created at right angles to the plane of symmetry of the\nmedium; while it would be possible to create a magnetic field under\nthe same conditions.\n\nThis consideration thus leads us to the discovery of new phenomena;\nbut it must be understood that it cannot of itself give us absolutely\nprecise notions as to the nature of these phenomena, nor disclose\ntheir order of magnitude.\n\n\nSec. 2. THE PRINCIPLE OF THE CONSERVATION OF ENERGY\n\nDominating not physics alone, but nearly every other science, the\nprinciple of the conservation of energy is justly considered as the\ngrandest conquest of contemporary thought. It shows us in a powerful\nlight the most diverse questions; it introduces order into the most\nvaried studies; it leads to a clear and coherent interpretation of\nphenomena which, without it, appear to have no connexion with each\nother; and it supplies precise and exact numerical relations between\nthe magnitudes which enter into these phenomena.\n\nThe boldest minds have an instinctive confidence in it, and it is the\nprinciple which has most stoutly resisted that assault which the\ndaring of a few theorists has lately directed to the overthrow of the\ngeneral principles of physics. At every new discovery, the first\nthought of physicists is to find out how it accords with the principle\nof the conservation of energy. The application of the principle,\nmoreover, never fails to give valuable hints on the new phenomenon,\nand often even suggests a complementary discovery. Up till now it\nseems never to have received a check, even the extraordinary\nproperties of radium not seriously contradicting it; also the general\nform in which it is enunciated gives it such a suppleness that it is\nno doubt very difficult to overthrow.\n\nI do not claim to set forth here the complete history of this\nprinciple, but I will endeavour to show with what pains it was born,\nhow it was kept back in its early days and then obstructed in its\ndevelopment by the unfavourable conditions of the surroundings in\nwhich it appeared. It first of all came, in fact, to oppose itself to\nthe reigning theories; but, little by little, it acted on these\ntheories, and they were modified under its pressure; then, in their\nturn, these theories reacted on it and changed its primitive form.\n\nIt had to be made less wide in order to fit into the classic frame,\nand was absorbed by mechanics; and if it thus became less general, it\ngained in precision what it lost in extent. When once definitely\nadmitted and classed, as it were, in the official domain of science,\nit endeavoured to burst its bonds and return to a more independent and\nlarger life. The history of this principle is similar to that of all\nevolutions.\n\nIt is well known that the conservation of energy was, at first,\nregarded from the point of view of the reciprocal transformations\nbetween heat and work, and that the principle received its first clear\nenunciation in the particular case of the principle of equivalence. It\nis, therefore, rightly considered that the scholars who were the first\nto doubt the material nature of caloric were the precursors of R.\nMayer; their ideas, however, were the same as those of the celebrated\nGerman doctor, for they sought especially to demonstrate that heat was\na mode of motion.\n\nWithout going back to early and isolated attempts like those of Daniel\nBernoulli, who, in his hydrodynamics, propounded the basis of the\nkinetic theory of gases, or the researches of Boyle on friction, we\nmay recall, to show how it was propounded in former times, a rather\nforgotten page of the _Memoire sur la Chaleur_, published in 1780 by\nLavoisier and Laplace: \"Other physicists,\" they wrote, after setting\nout the theory of caloric, \"think that heat is nothing but the result\nof the insensible vibrations of matter.... In the system we are now\nexamining, heat is the _vis viva_ resulting from the insensible\nmovements of the molecules of a body; it is the sum of the products of\nthe mass of each molecule by the square of its velocity.... We shall\nnot decide between the two preceding hypotheses; several phenomena\nseem to support the last mentioned--for instance, that of the heat\nproduced by the friction of two solid bodies. But there are others\nwhich are more simply explained by the first, and perhaps they both\noperate at once.\" Most of the physicists of that period, however, did\nnot share the prudent doubts of Lavoisier and Laplace. They admitted,\nwithout hesitation, the first hypothesis; and, four years after the\nappearance of the _Memoire sur la Chaleur_, Sigaud de Lafond, a\nprofessor of physics of great reputation, wrote: \"Pure Fire, free from\nall state of combination, seems to be an assembly of particles of a\nsimple, homogeneous, and absolutely unalterable matter, and all the\nproperties of this element indicate that these particles are\ninfinitely small and free, that they have no sensible cohesion, and\nthat they are moved in every possible direction by a continual and\nrapid motion which is essential to them.... The extreme tenacity and\nthe surprising mobility of its molecules are manifestly shown by the\nease with which it penetrates into the most compact bodies and by its\ntendency to put itself in equilibrium throughout all bodies near to\nit.\"\n\nIt must be acknowledged, however, that the idea of Lavoisier and\nLaplace was rather vague and even inexact on one important point. They\nadmitted it to be evident that \"all variations of heat, whether real\nor apparent, undergone by a bodily system when changing its state, are\nproduced in inverse order when the system passes back to its original\nstate.\" This phrase is the very denial of equivalence where these\nchanges of state are accompanied by external work.\n\nLaplace, moreover, himself became later a very convinced partisan of\nthe hypothesis of the material nature of caloric, and his immense\nauthority, so fortunate in other respects for the development of\nscience, was certainly in this case the cause of the retardation of\nprogress.\n\nThe names of Young, Rumford, Davy, are often quoted among those\nphysicists who, at the commencement of the nineteenth century, caught\nsight of the new truths as to the nature of heat. To these names is\nvery properly added that of Sadi Carnot. A note found among his papers\nunquestionably proves that, before 1830, ideas had occurred to him\nfrom which it resulted that in producing work an equivalent amount of\nheat was destroyed. But the year 1842 is particularly memorable in the\nhistory of science as the year in which Jules Robert Mayer succeeded,\nby an entirely personal effort, in really enunciating the principle of\nthe conservation of energy. Chemists recall with just pride that the\n_Remarques sur les forces de la nature animee_, contemptuously\nrejected by all the journals of physics, were received and published\nin the _Annalen_ of Liebig. We ought never to forget this example,\nwhich shows with what difficulty a new idea contrary to the classic\ntheories of the period succeeds in coming to the front; but\nextenuating circumstances may be urged on behalf of the physicists.\n\nRobert Mayer had a rather insufficient mathematical education, and his\nMemoirs, the _Remarques_, as well as the ulterior publications,\n_Memoire sur le mouvement organique et la nutrition_ and the\n_Materiaux pour la dynamique du ciel_, contain, side by side with very\nprofound ideas, evident errors in mechanics. Thus it often happens\nthat discoveries put forward in a somewhat vague manner by adventurous\nminds not overburdened by the heavy baggage of scientific erudition,\nwho audaciously press forward in advance of their time, fall into\nquite intelligible oblivion until rediscovered, clarified, and put\ninto shape by slower but surer seekers. This was the case with the\nideas of Mayer. They were not understood at first sight, not only on\naccount of their originality, but also because they were couched in\nincorrect language.\n\nMayer was, however, endowed with a singular strength of thought; he\nexpressed in a rather confused manner a principle which, for him, had\na generality greater than mechanics itself, and so his discovery was\nin advance not only of his own time but of half the century. He may\njustly be considered the founder of modern energetics.\n\nFreed from the obscurities which prevented its being clearly\nperceived, his idea stands out to-day in all its imposing simplicity.\nYet it must be acknowledged that if it was somewhat denaturalised by\nthose who endeavoured to adapt it to the theories of mechanics, and if\nit at first lost its sublime stamp of generality, it thus became\nfirmly fixed and consolidated on a more stable basis.\n\nThe efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the\nprinciple of the conservation of energy into mechanics, were far from\nuseless. These illustrious physicists succeeded in giving a more\nprecise form to its numerous applications; and their attempts thus\ncontributed, by reaction, to give a fresh impulse to mechanics, and\nallowed it to be linked to a more general order of facts. If\nenergetics has not been able to be included in mechanics, it seems\nindeed that the attempt to include mechanics in energetics was not in\nvain.\n\nIn the middle of the last century, the explanation of all natural\nphenomena seemed more and more referable to the case of central\nforces. Everywhere it was thought that reciprocal actions between\nmaterial points could be perceived, these points being attracted or\nrepelled by each other with an intensity depending only on their\ndistance or their mass. If, to a system thus composed, the laws of the\nclassical mechanics are applied, it is shown that half the sum of the\nproduct of the masses by the square of the velocities, to which is\nadded the work which might be accomplished by the forces to which the\nsystem would be subject if it returned from its actual to its initial\nposition, is a sum constant in quantity.\n\nThis sum, which is the mechanical energy of the system, is therefore\nan invariable quantity in all the states to which it may be brought by\nthe interaction of its various parts, and the word energy well\nexpresses a capital property of this quantity. For if two systems are\nconnected in such a way that any change produced in the one\nnecessarily brings about a change in the other, there can be no\nvariation in the characteristic quantity of the second except so far\nas the characteristic quantity of the first itself varies--on\ncondition, of course, that the connexions are made in such a manner as\nto introduce no new force. It will thus be seen that this quantity\nwell expresses the capacity possessed by a system for modifying the\nstate of a neighbouring system to which we may suppose it connected.\n\nNow this theorem of pure mechanics was found wanting every time\nfriction took place--that is to say, in all really observable cases.\nThe more perceptible the friction, the more considerable the\ndifference; but, in addition, a new phenomenon always appeared and\nheat was produced. By experiments which are now classic, it became\nestablished that the quantity of heat thus created independently of\nthe nature of the bodies is always (provided no other phenomena\nintervene) proportional to the energy which has disappeared.\nReciprocally, also, heat may disappear, and we always find a constant\nrelation between the quantities of heat and work which mutually\nreplace each other.\n\nIt is quite clear that such experiments do not prove that heat is\nwork. We might just as well say that work is heat. It is making a\ngratuitous hypothesis to admit this reduction of heat to mechanism;\nbut this hypothesis was so seductive, and so much in conformity with\nthe desire of nearly all physicists to arrive at some sort of unity in\nnature, that they made it with eagerness and became unreservedly\nconvinced that heat was an active internal force.\n\nTheir error was not in admitting this hypothesis; it was a legitimate\none since it has proved very fruitful. But some of them committed the\nfault of forgetting that it was an hypothesis, and considered it a\ndemonstrated truth. Moreover, they were thus brought to see in\nphenomena nothing but these two particular forms of energy which in\ntheir minds were easily identified with each other.\n\nFrom the outset, however, it became manifest that the principle is\napplicable to cases where heat plays only a parasitical part. There\nwere thus discovered, by translating the principle of equivalence,\nnumerical relations between the magnitudes of electricity, for\ninstance, and the magnitudes of mechanics. Heat was a sort of variable\nintermediary convenient for calculation, but introduced in a\nroundabout way and destined to disappear in the final result.\n\nVerdet, who, in lectures which have rightly remained celebrated,\ndefined with remarkable clearness the new theories, said, in 1862:\n\"Electrical phenomena are always accompanied by calorific\nmanifestations, of which the study belongs to the mechanical theory of\nheat. This study, moreover, will not only have the effect of making\nknown to us interesting facts in electricity, but will throw some\nlight on the phenomena of electricity themselves.\"\n\nThe eminent professor was thus expressing the general opinion of his\ncontemporaries, but he certainly seemed to have felt in advance that\nthe new theory was about to penetrate more deeply into the inmost\nnature of things. Three years previously, Rankine also had put forth\nsome very remarkable ideas the full meaning of which was not at first\nwell understood. He it was who comprehended the utility of employing a\nmore inclusive term, and invented the phrase energetics. He also\nendeavoured to create a new doctrine of which rational mechanics\nshould be only a particular case; and he showed that it was possible\nto abandon the ideas of atoms and central forces, and to construct a\nmore general system by substituting for the ordinary consideration of\nforces that of the energy which exists in all bodies, partly in an\nactual, partly in a potential state.\n\nBy giving more precision to the conceptions of Rankine, the physicists\nof the end of the nineteenth century were brought to consider that in\nall physical phenomena there occur apparitions and disappearances\nwhich are balanced by various energies. It is natural, however, to\nsuppose that these equivalent apparitions and disappearances\ncorrespond to transformations and not to simultaneous creations and\ndestructions. We thus represent energy to ourselves as taking\ndifferent forms--mechanical, electrical, calorific, and chemical--\ncapable of changing one into the other, but in such a way that the\nquantitative value always remains the same. In like manner a bank\ndraft may be represented by notes, gold, silver, or bullion. The\nearliest known form of energy, _i.e._ work, will serve as the standard\nas gold serves as the monetary standard, and energy in all its forms\nwill be estimated by the corresponding work. In each particular case\nwe can strictly define and measure, by the correct application of the\nprinciple of the conservation of energy, the quantity of energy\nevolved under a given form.\n\nWe can thus arrange a machine comprising a body capable of evolving\nthis energy; then we can force all the organs of this machine to\ncomplete an entirely closed cycle, with the exception of the body\nitself, which, however, has to return to such a state that all the\nvariables from which this state depends resume their initial values\nexcept the particular variable to which the evolution of the energy\nunder consideration is linked. The difference between the work thus\naccomplished and that which would have been obtained if this variable\nalso had returned to its original value, is the measure of the energy\nevolved.\n\nIn the same way that, in the minds of mechanicians, all forces of\nwhatever origin, which are capable of compounding with each other and\nof balancing each other, belong to the same category of beings, so for\nmany physicists energy is a sort of entity which we find under various\naspects. There thus exists for them a world, which comes in some way\nto superpose itself upon the world of matter--that is to say, the\nworld of energy, dominated in its turn by a fundamental law similar to\nthat of Lavoisier.[5] This conception, as we have already seen, passes\nthe limit of experience; but others go further still. Absorbed in the\ncontemplation of this new world, they succeed in persuading themselves\nthat the old world of matter has no real existence and that energy is\nsufficient by itself to give us a complete comprehension of the\nUniverse and of all the phenomena produced in it. They point out that\nall our sensations correspond to changes of energy, and that\neverything apparent to our senses is, in truth, energy. The famous\nexperiment of the blows with a stick by which it was demonstrated to a\nsceptical philosopher that an outer world existed, only proves, in\nreality, the existence of energy, and not that of matter. The stick in\nitself is inoffensive, as Professor Ostwald remarks, and it is its\n_vis viva_, its kinetic energy, which is painful to us; while if we\npossessed a speed equal to its own, moving in the same direction, it\nwould no longer exist so far as our sense of touch is concerned.\n\n[Footnote 5: \"Nothing is created; nothing is lost\"--ED.]\n\nOn this hypothesis, matter would only be the capacity for kinetic\nenergy, its pretended impenetrability energy of volume, and its weight\nenergy of position in the particular form which presents itself in\nuniversal gravitation; nay, space itself would only be known to us by\nthe expenditure of energy necessary to penetrate it. Thus in all\nphysical phenomena we should only have to regard the quantities of\nenergy brought into play, and all the equations which link the\nphenomena to one another would have no meaning but when they apply to\nexchanges of energy. For energy alone can be common to all phenomena.\n\nThis extreme manner of regarding things is seductive by its\noriginality, but appears somewhat insufficient if, after enunciating\ngeneralities, we look more closely into the question. From the\nphilosophical point of view it may, moreover, seem difficult not to\nconclude, from the qualities which reveal, if you will, the varied\nforms of energy, that there exists a substance possessing these\nqualities. This energy, which resides in one region, and which\ntransports itself from one spot to another, forcibly brings to mind,\nwhatever view we may take of it, the idea of matter.\n\nHelmholtz endeavoured to construct a mechanics based on the idea of\nenergy and its conservation, but he had to invoke a second law, the\nprinciple of least action. If he thus succeeded in dispensing with the\nhypothesis of atoms, and in showing that the new mechanics gave us to\nunderstand the impossibility of certain movements which, according to\nthe old, ought to have been but never were experimentally produced, he\nwas only able to do so because the principle of least action necessary\nfor his theory became evident in the case of those irreversible\nphenomena which alone really exist in Nature. The energetists have\nthus not succeeded in forming a thoroughly sound system, but their\nefforts have at all events been partly successful. Most physicists are\nof their opinion, that kinetic energy is only a particular variety of\nenergy to which we have no right to wish to connect all its other\nforms.\n\nIf these forms showed themselves to be innumerable throughout the\nUniverse, the principle of the conservation of energy would, in fact,\nlose a great part of its importance. Every time that a certain\nquantity of energy seemed to appear or disappear, it would always be\npermissible to suppose that an equivalent quantity had appeared or\ndisappeared somewhere else under a new form; and thus the principle\nwould in a way vanish. But the known forms of energy are fairly\nrestricted in number, and the necessity of recognising new ones seldom\nmakes itself felt. We shall see, however, that to explain, for\ninstance, the paradoxical properties of radium and to re-establish\nconcord between these properties and the principle of the conservation\nof energy, certain physicists have recourse to the hypothesis that\nradium borrows an unknown energy from the medium in which it is\nplunged. This hypothesis, however, is in no way necessary; and in a\nfew other rare cases in which similar hypotheses have had to be set\nup, experiment has always in the long run enabled us to discover some\nphenomenon which had escaped the first observers and which corresponds\nexactly to the variation of energy first made evident.\n\nOne difficulty, however, arises from the fact that the principle ought\nonly to be applied to an isolated system. Whether we imagine actions\nat a distance or believe in intermediate media, we must always\nrecognise that there exist no bodies in the world incapable of acting\non each other, and we can never affirm that some modification in the\nenergy of a given place may not have its echo in some unknown spot\nafar off. This difficulty may sometimes render the value of the\nprinciple rather illusory.\n\nSimilarly, it behoves us not to receive without a certain distrust the\nextension by certain philosophers to the whole Universe, of a property\ndemonstrated for those restricted systems which observation can alone\nreach. We know nothing of the Universe as a whole, and every\ngeneralization of this kind outruns in a singular fashion the limit of\nexperiment.\n\nEven reduced to the most modest proportions, the principle of the\nconservation of energy retains, nevertheless, a paramount importance;\nand it still preserves, if you will, a high philosophical value. M.J.\nPerrin justly points out that it gives us a form under which we are\nexperimentally able to grasp causality, and that it teaches us that a\nresult has to be purchased at the cost of a determined effort.\n\nWe can, in fact, with M. Perrin and M. Langevin, represent this in a\nway which puts this characteristic in evidence by enunciating it as\nfollows: \"If at the cost of a change C we can obtain a change K, there\nwill never be acquired at the same cost, whatever the mechanism\nemployed, first the change K and in addition some other change, unless\nthis latter be one that is otherwise known to cost nothing to produce\nor to destroy.\" If, for instance, the fall of a weight can be\naccompanied, without anything else being produced, by another\ntransformation--the melting of a certain mass of ice, for example--it\nwill be impossible, no matter how you set about it or whatever the\nmechanism used, to associate this same transformation with the melting\nof another weight of ice.\n\nWe can thus, in the transformation in question, obtain an appropriate\nnumber which will sum up that which may be expected from the external\neffect, and can give, so to speak, the price at which this\ntransformation is bought, measure its invariable value by a common\nmeasure (for instance, the melting of the ice), and, without any\nambiguity, define the energy lost during the transformation as\nproportional to the mass of ice which can be associated with it. This\nmeasure is, moreover, independent of the particular phenomenon taken\nas the common measure.\n\n\nSec. 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS\n\nThe principle of Carnot, of a nature analogous to the principle of the\nconservation of energy, has also a similar origin. It was first\nenunciated, like the last named, although prior to it in time, in\nconsequence of considerations which deal only with heat and mechanical\nwork. Like it, too, it has evolved, grown, and invaded the entire\ndomain of physics. It may be interesting to examine rapidly the\nvarious phases of this evolution. The origin of the principle of\nCarnot is clearly determined, and it is very rare to be able to go\nback thus certainly to the source of a discovery. Sadi Carnot had,\ntruth to say, no precursor. In his time heat engines were not yet very\ncommon, and no one had reflected much on their theory. He was\ndoubtless the first to propound to himself certain questions, and\ncertainly the first to solve them.\n\nIt is known how, in 1824, in his _Reflexions sur la puissance motrice\ndu feu_, he endeavoured to prove that \"the motive power of heat is\nindependent of the agents brought into play for its realization,\" and\nthat \"its quantity is fixed solely by the temperature of the bodies\nbetween which, in the last resort, the transport of caloric is\neffected\"--at least in all engines in which \"the method of developing\nthe motive power attains the perfection of which it is capable\"; and\nthis is, almost textually, one of the enunciations of the principle at\nthe present day. Carnot perceived very clearly the great fact that, to\nproduce work by heat, it is necessary to have at one's disposal a fall\nof temperature. On this point he expresses himself with perfect\nclearness: \"The motive power of a fall of water depends on its height\nand on the quantity of liquid; the motive power of heat depends also\non the quantity of caloric employed, and on what might be called--in\nfact, what we shall call--the height of fall, that is to say, the\ndifference in temperature of the bodies between which the exchange of\ncaloric takes place.\"\n\nStarting with this idea, he endeavours to demonstrate, by associating\ntwo engines capable of working in a reversible cycle, that the\nprinciple is founded on the impossibility of perpetual motion.\n\nHis memoir, now celebrated, did not produce any great sensation, and\nit had almost fallen into deep oblivion, which, in consequence of\nthe discovery of the principle of equivalence, might have seemed\nperfectly justified. Written, in fact, on the hypothesis of the\nindestructibility of caloric, it was to be expected that this memoir\nshould be condemned in the name of the new doctrine, that is, of the\nprinciple recently brought to light.\n\nIt was really making a new discovery to establish that Carnot's\nfundamental idea survived the destruction of the hypothesis on the\nnature of heat, on which he seemed to rely. As he no doubt himself\nperceived, his idea was quite independent of this hypothesis, since,\nas we have seen, he was led to surmise that heat could disappear; but\nhis demonstrations needed to be recast and, in some points, modified.\n\nIt is to Clausius that was reserved the credit of rediscovering the\nprinciple, and of enunciating it in language conformable to the new\ndoctrines, while giving it a much greater generality. The postulate\narrived at by experimental induction, and which must be admitted\nwithout demonstration, is, according to Clausius, that in a series of\ntransformations in which the final is identical with the initial\nstage, it is impossible for heat to pass from a colder to a warmer\nbody unless some other accessory phenomenon occurs at the same time.\n\nStill more correctly, perhaps, an enunciation can be given of the\npostulate which, in the main, is analogous, by saying: A heat motor,\nwhich after a series of transformations returns to its initial state,\ncan only furnish work if there exist at least two sources of heat, and\nif a certain quantity of heat is given to one of the sources, which\ncan never be the hotter of the two. By the expression \"source of\nheat,\" we mean a body exterior to the system and capable of furnishing\nor withdrawing heat from it.\n\nStarting with this principle, we arrive, as does Clausius, at the\ndemonstration that the output of a reversible machine working between\ntwo given temperatures is greater than that of any non-reversible\nengine, and that it is the same for all reversible machines working\nbetween these two temperatures.\n\nThis is the very proposition of Carnot; but the proposition thus\nstated, while very useful for the theory of engines, does not yet\npresent any very general interest. Clausius, however, drew from it\nmuch more important consequences. First, he showed that the principle\nconduces to the definition of an absolute scale of temperature; and\nthen he was brought face to face with a new notion which allows a\nstrong light to be thrown on the questions of physical equilibrium. I\nrefer to entropy.\n\nIt is still rather difficult to strip entirely this very important\nnotion of all analytical adornment. Many physicists hesitate to\nutilize it, and even look upon it with some distrust, because they see\nin it a purely mathematical function without any definite physical\nmeaning. Perhaps they are here unduly severe, since they often admit\ntoo easily the objective existence of quantities which they cannot\ndefine. Thus, for instance, it is usual almost every day to speak of\nthe heat possessed by a body. Yet no body in reality possesses a\ndefinite quantity of heat even relatively to any initial state; since\nstarting from this point of departure, the quantities of heat it may\nhave gained or lost vary with the road taken and even with the means\nemployed to follow it. These expressions of heat gained or lost are,\nmoreover, themselves evidently incorrect, for heat can no longer be\nconsidered as a sort of fluid passing from one body to another.\n\nThe real reason which makes entropy somewhat mysterious is that this\nmagnitude does not fall directly under the ken of any of our senses;\nbut it possesses the true characteristic of a concrete physical\nmagnitude, since it is, in principle at least, measurable. Various\nauthors of thermodynamical researches, amongst whom M. Mouret should\nbe particularly mentioned, have endeavoured to place this\ncharacteristic in evidence.\n\nConsider an isothermal transformation. Instead of leaving the heat\nabandoned by the body subjected to the transformation--water\ncondensing in a state of saturated vapour, for instance--to pass\ndirectly into an ice calorimeter, we can transmit this heat to the\ncalorimeter by the intermediary of a reversible Carnot engine. The\nengine having absorbed this quantity of heat, will only give back to\nthe ice a lesser quantity of heat; and the weight of the melted ice,\ninferior to that which might have been directly given back, will serve\nas a measure of the isothermal transformation thus effected. It can be\neasily shown that this measure is independent of the apparatus used.\nIt consequently becomes a numerical element characteristic of the body\nconsidered, and is called its entropy. Entropy, thus defined, is a\nvariable which, like pressure or volume, might serve concurrently with\nanother variable, such as pressure or volume, to define the state of a\nbody.\n\nIt must be perfectly understood that this variable can change in an\nindependent manner, and that it is, for instance, distinct from the\nchange of temperature. It is also distinct from the change which\nconsists in losses or gains of heat. In chemical reactions, for\nexample, the entropy increases without the substances borrowing any\nheat. When a perfect gas dilates in a vacuum its entropy increases,\nand yet the temperature does not change, and the gas has neither been\nable to give nor receive heat. We thus come to conceive that a\nphysical phenomenon cannot be considered known to us if the variation\nof entropy is not given, as are the variations of temperature and of\npressure or the exchanges of heat. The change of entropy is, properly\nspeaking, the most characteristic fact of a thermal change.\n\nIt is important, however, to remark that if we can thus easily define\nand measure the difference of entropy between two states of the same\nbody, the value found depends on the state arbitrarily chosen as the\nzero point of entropy; but this is not a very serious difficulty, and\nis analogous to that which occurs in the evaluation of other physical\nmagnitudes--temperature, potential, etc.\n\nA graver difficulty proceeds from its not being possible to define a\ndifference, or an equality, of entropy between two bodies chemically\ndifferent. We are unable, in fact, to pass by any means, reversible or\nnot, from one to the other, so long as the transmutation of matter is\nregarded as impossible; but it is well understood that it is\nnevertheless possible to compare the variations of entropy to which\nthese two bodies are both of them individually subject.\n\nNeither must we conceal from ourselves that the definition supposes,\nfor a given body, the possibility of passing from one state to another\nby a reversible transformation. Reversibility is an ideal and extreme\ncase which cannot be realized, but which can be approximately attained\nin many circumstances. So with gases and with perfectly elastic\nbodies, we effect sensibly reversible transformations, and changes\nof physical state are practically reversible. The discoveries of\nSainte-Claire Deville have brought many chemical phenomena into a\nsimilar category, and reactions such as solution, which used to be\nformerly the type of an irreversible phenomenon, may now often be\neffected by sensibly reversible means. Be that as it may, when once the\ndefinition is admitted, we arrive, by taking as a basis the principles\nset forth at the inception, at the demonstration of the celebrated\ntheorem of Clausius: _The entropy of a thermally isolated system\ncontinues to increase incessantly._\n\nIt is very evident that the theorem can only be worth applying in\ncases where the entropy can be exactly defined; but, even when thus\nlimited, the field still remains vast, and the harvest which we can\nthere reap is very abundant.\n\nEntropy appears, then, as a magnitude measuring in a certain way the\nevolution of a system, or, at least, as giving the direction of this\nevolution. This very important consequence certainly did not escape\nClausius, since the very name of entropy, which he chose to designate\nthis magnitude, itself signifies evolution. We have succeeded in\ndefining this entropy by demonstrating, as has been said, a certain\nnumber of propositions which spring from the postulate of Clausius; it\nis, therefore, natural to suppose that this postulate itself contains\n_in potentia_ the very idea of a necessary evolution of physical\nsystems. But as it was first enunciated, it contains it in a deeply\nhidden way.\n\nNo doubt we should make the principle of Carnot appear in an\ninteresting light by endeavouring to disengage this fundamental idea,\nand by placing it, as it were, in large letters. Just as, in\nelementary geometry, we can replace the postulate of Euclid by other\nequivalent propositions, so the postulate of thermodynamics is not\nnecessarily fixed, and it is instructive to try to give it the most\ngeneral and suggestive character.\n\nMM. Perrin and Langevin have made a successful attempt in this\ndirection. M. Perrin enunciates the following principle: _An isolated\nsystem never passes twice through the same state_. In this form, the\nprinciple affirms that there exists a necessary order in the\nsuccession of two phenomena; that evolution takes place in a\ndetermined direction. If you prefer it, it may be thus stated: _Of two\nconverse transformations unaccompanied by any external effect, one\nonly is possible_. For instance, two gases may diffuse themselves one\nin the other in constant volume, but they could not conversely\nseparate themselves spontaneously.\n\nStarting from the principle thus put forward, we make the logical\ndeduction that one cannot hope to construct an engine which should\nwork for an indefinite time by heating a hot source and by cooling a\ncold one. We thus come again into the route traced by Clausius, and\nfrom this point we may follow it strictly.\n\nWhatever the point of view adopted, whether we regard the proposition\nof M. Perrin as the corollary of another experimental postulate, or\nwhether we consider it as a truth which we admit _a priori_ and verify\nthrough its consequences, we are led to consider that in its entirety\nthe principle of Carnot resolves itself into the idea that we cannot\ngo back along the course of life, and that the evolution of a system\nmust follow its necessary progress.\n\nClausius and Lord Kelvin have drawn from these considerations certain\nwell-known consequences on the evolution of the Universe. Noticing\nthat entropy is a property added to matter, they admit that there is\nin the world a total amount of entropy; and as all real changes which\nare produced in any system correspond to an increase of entropy, it\nmay be said that the entropy of the world is continually increasing.\nThus the quantity of energy existing in the Universe remains constant,\nbut transforms itself little by little into heat uniformly distributed\nat a temperature everywhere identical. In the end, therefore, there\nwill be neither chemical phenomena nor manifestation of life; the\nworld will still exist, but without motion, and, so to speak, dead.\n\nThese consequences must be admitted to be very doubtful; we cannot in\nany certain way apply to the Universe, which is not a finite system, a\nproposition demonstrated, and that not unreservedly, in the sharply\nlimited case of a finite system. Herbert Spencer, moreover, in his\nbook on _First Principles_, brings out with much force the idea that,\neven if the Universe came to an end, nothing would allow us to\nconclude that, once at rest, it would remain so indefinitely. We may\nrecognise that the state in which we are began at the end of a former\nevolutionary period, and that the end of the existing era will mark\nthe beginning of a new one.\n\nLike an elastic and mobile object which, thrown into the air, attains\nby degrees the summit of its course, then possesses a zero velocity\nand is for a moment in equilibrium, and then falls on touching the\nground to rebound, so the world should be subjected to huge\noscillations which first bring it to a maximum of entropy till the\nmoment when there should be produced a slow evolution in the contrary\ndirection bringing it back to the state from which it started. Thus,\nin the infinity of time, the life of the Universe proceeds without\nreal stop.\n\nThis conception is, moreover, in accordance with the view certain\nphysicists take of the principle of Carnot. We shall see, for example,\nthat in the kinetic theory we are led to admit that, after waiting\nsufficiently long, we can witness the return of the various states\nthrough which a mass of gas, for example, has passed in its series of\ntransformations.\n\nIf we keep to the present era, evolution has a fixed direction--that\nwhich leads to an increase of entropy; and it is possible to enquire,\nin any given system to what physical manifestations this increase\ncorresponds. We note that kinetic, potential, electrical, and chemical\nforms of energy have a great tendency to transform themselves into\ncalorific energy. A chemical reaction, for example, gives out energy;\nbut if the reaction is not produced under very special conditions,\nthis energy immediately passes into the calorific form. This is so\ntrue, that chemists currently speak of the heat given out by reactions\ninstead of regarding the energy disengaged in general.\n\nIn all these transformations the calorific energy obtained has not,\nfrom a practical point of view, the same value at which it started.\nOne cannot, in fact, according to the principle of Carnot, transform\nit integrally into mechanical energy, since the heat possessed by a\nbody can only yield work on condition that a part of it falls on a\nbody with a lower temperature. Thus appears the idea that energies\nwhich exchange with each other and correspond to equal quantities have\nnot the same qualitative value. Form has its importance, and there are\npersons who prefer a golden louis to four pieces of five francs. The\nprinciple of Carnot would thus lead us to consider a certain\nclassification of energies, and would show us that, in the\ntransformations possible, these energies always tend to a sort of\ndiminution of quality--that is, to a _degradation_.\n\nIt would thus reintroduce an element of differentiation of which it\nseems very difficult to give a mechanical explanation. Certain\nphilosophers and physicists see in this fact a reason which condemns\n_a priori_ all attempts made to give a mechanical explanation of the\nprinciple of Carnot.\n\nIt is right, however, not to exaggerate the importance that should be\nattributed to the phrase degraded energy. If the heat is not\nequivalent to the work, if heat at 99 deg. is not equivalent to heat at\n100 deg., that means that we cannot in practice construct an engine which\nshall transform all this heat into work, or that, for the same cold\nsource, the output is greater when the temperature of the hot source\nis higher; but if it were possible that this cold source had itself\nthe temperature of absolute zero, the whole heat would reappear in the\nform of work. The case here considered is an ideal and extreme case,\nand we naturally cannot realize it; but this consideration suffices to\nmake it plain that the classification of energies is a little\narbitrary and depends more, perhaps, on the conditions in which\nmankind lives than on the inmost nature of things.\n\nIn fact, the attempts which have often been made to refer the\nprinciple of Carnot to mechanics have not given convincing results. It\nhas nearly always been necessary to introduce into the attempt some\nnew hypothesis independent of the fundamental hypotheses of ordinary\nmechanics, and equivalent, in reality, to one of the postulates on\nwhich the ordinary exposition of the second law of thermodynamics is\nfounded. Helmholtz, in a justly celebrated theory, endeavoured to fit\nthe principle of Carnot into the principle of least action; but the\ndifficulties regarding the mechanical interpretation of the\nirreversibility of physical phenomena remain entire. Looking at the\nquestion, however, from the point of view at which the partisans of\nthe kinetic theories of matter place themselves, the principle is\nviewed in a new aspect. Gibbs and afterwards Boltzmann and Professor\nPlanck have put forward some very interesting ideas on this subject.\nBy following the route they have traced, we come to consider the\nprinciple as pointing out to us that a given system tends towards the\nconfiguration presented by the maximum probability, and, numerically,\nthe entropy would even be the logarithm of this probability. Thus two\ndifferent gaseous masses, enclosed in two separate receptacles which\nhave just been placed in communication, diffuse themselves one through\nthe other, and it is highly improbable that, in their mutual shocks,\nboth kinds of molecules should take a distribution of velocities which\nreduce them by a spontaneous phenomenon to the initial state.\n\nWe should have to wait a very long time for so extraordinary a\nconcourse of circumstances, but, in strictness, it would not be\nimpossible. The principle would only be a law of probability. Yet this\nprobability is all the greater the more considerable is the number of\nmolecules itself. In the phenomena habitually dealt with, this number\nis such that, practically, the variation of entropy in a constant\nsense takes, so to speak, the character of absolute certainty.\n\nBut there may be exceptional cases where the complexity of the system\nbecomes insufficient for the application of the principle of Carnot;--\nas in the case of the curious movements of small particles suspended\nin a liquid which are known by the name of Brownian movements and can\nbe observed under the microscope. The agitation here really seems, as\nM. Gouy has remarked, to be produced and continued indefinitely,\nregardless of any difference in temperature; and we seem to witness\nthe incessant motion, in an isothermal medium, of the particles which\nconstitute matter. Perhaps, however, we find ourselves already in\nconditions where the too great simplicity of the distribution of the\nmolecules deprives the principle of its value.\n\nM. Lippmann has in the same way shown that, on the kinetic hypothesis,\nit is possible to construct such mechanisms that we can so take\ncognizance of molecular movements that _vis viva_ can be taken from\nthem. The mechanisms of M. Lippmann are not, like the celebrated\napparatus at one time devised by Maxwell, purely hypothetical. They do\nnot suppose a partition with a hole impossible to be bored through\nmatter where the molecular spaces would be larger than the hole\nitself. They have finite dimensions. Thus M. Lippmann considers a vase\nfull of oxygen at a constant temperature. In the interior of this vase\nis placed a small copper ring, and the whole is set in a magnetic\nfield. The oxygen molecules are, as we know, magnetic, and when\npassing through the interior of the ring they produce in this ring an\ninduced current. During this time, it is true, other molecules emerge\nfrom the space enclosed by the circuit; but the two effects do not\ncounterbalance each other, and the resulting current is maintained.\nThere is elevation of temperature in the circuit in accordance with\nJoule's law; and this phenomenon, under such conditions, is\nincompatible with the principle of Carnot.\n\nIt is possible--and that, I think, is M. Lippmann's idea--to draw from\nhis very ingenious criticism an objection to the kinetic theory, if we\nadmit the absolute value of the principle; but we may also suppose\nthat here again we are in presence of a system where the prescribed\nconditions diminish the complexity and render it, consequently, less\nprobable that the evolution is always effected in the same direction.\n\nIn whatever way you look at it, the principle of Carnot furnishes, in\nthe immense majority of cases, a very sure guide in which physicists\ncontinue to have the most entire confidence.\n\n\nSec. 4. THERMODYNAMICS\n\nTo apply the two fundamental principles of thermodynamics, various\nmethods may be employed, equivalent in the main, but presenting as the\ncases vary a greater or less convenience.\n\nIn recording, with the aid of the two quantities, energy and entropy,\nthe relations which translate analytically the two principles, we\nobtain two relations between the coefficients which occur in a given\nphenomenon; but it may be easier and also more suggestive to employ\nvarious functions of these quantities. In a memoir, of which some\nextracts appeared as early as 1869, a modest scholar, M. Massieu,\nindicated in particular a remarkable function which he termed a\ncharacteristic function, and by the employment of which calculations\nare simplified in certain cases.\n\nIn the same way J.W. Gibbs, in 1875 and 1878, then Helmholtz in 1882,\nand, in France, M. Duhem, from the year 1886 onward, have published\nworks, at first ill understood, of which the renown was, however,\nconsiderable in the sequel, and in which they made use of analogous\nfunctions under the names of available energy, free energy, or\ninternal thermodynamic potential. The magnitude thus designated,\nattaching, as a consequence of the two principles, to all states of\nthe system, is perfectly determined when the temperature and other\nnormal variables are known. It allows us, by calculations often very\neasy, to fix the conditions necessary and sufficient for the\nmaintenance of the system in equilibrium by foreign bodies taken at\nthe same temperature as itself.\n\nOne may hope to constitute in this way, as M. Duhem in a long and\nremarkable series of operations has specially endeavoured to do, a\nsort of general mechanics which will enable questions of statics to be\ntreated with accuracy, and all the conditions of equilibrium of the\nsystem, including the calorific properties, to be determined. Thus,\nordinary statics teaches us that a liquid with its vapour on the top\nforms a system in equilibrium, if we apply to the two fluids a\npressure depending on temperature alone. Thermodynamics will furnish\nus, in addition, with the expression of the heat of vaporization and\nof, the specific heats of the two saturated fluids.\n\nThis new study has given us also most valuable information on\ncompressible fluids and on the theory of elastic equilibrium. Added to\ncertain hypotheses on electric or magnetic phenomena, it gives a\ncoherent whole from which can be deduced the conditions of electric or\nmagnetic equilibrium; and it illuminates with a brilliant light the\ncalorific laws of electrolytic phenomena.\n\nBut the most indisputable triumph of this thermodynamic statics is the\ndiscovery of the laws which regulate the changes of physical state or\nof chemical constitution. J.W. Gibbs was the author of this immense\nprogress. His memoir, now celebrated, on \"the equilibrium of\nheterogeneous substances,\" concealed in 1876 in a review at that time\nof limited circulation, and rather heavy to read, seemed only to\ncontain algebraic theorems applicable with difficulty to reality. It\nis known that Helmholtz independently succeeded, a few years later, in\nintroducing thermodynamics into the domain of chemistry by his\nconception of the division of energy into free and into bound energy:\nthe first, capable of undergoing all transformations, and particularly\nof transforming itself into external action; the second, on the other\nhand, bound, and only manifesting itself by giving out heat. When we\nmeasure chemical energy, we ordinarily let it fall wholly into the\ncalorific form; but, in reality, it itself includes both parts, and it\nis the variation of the free energy and not that of the total energy\nmeasured by the integral disengagement of heat, the sign of which\ndetermines the direction in which the reactions are effected.\n\nBut if the principle thus enunciated by Helmholtz as a consequence of\nthe laws of thermodynamics is at bottom identical with that discovered\nby Gibbs, it is more difficult of application and is presented under a\nmore mysterious aspect. It was not until M. Van der Waals exhumed the\nmemoir of Gibbs, when numerous physicists or chemists, most of them\nDutch--Professor Van t'Hoff, Bakhius Roozeboom, and others--utilized\nthe rules set forth in this memoir for the discussion of the most\ncomplicated chemical reactions, that the extent of the new laws was\nfully understood.\n\nThe chief rule of Gibbs is the one so celebrated at the present day\nunder the name of the Phase Law. We know that by phases are designated\nthe homogeneous substances into which a system is divided; thus\ncarbonate of lime, lime, and carbonic acid gas are the three phases of\na system which comprises Iceland spar partially dissociated into lime\nand carbonic acid gas. The number of phases added to the number of\nindependent components--that is to say, bodies whose mass is left\narbitrary by the chemical formulas of the substances entering into the\nreaction--fixes the general form of the law of equilibrium of the\nsystem; that is to say, the number of quantities which, by their\nvariations (temperature and pressure), would be of a nature to modify\nits equilibrium by modifying the constitution of the phases.\n\nSeveral authors, M. Raveau in particular, have indeed given very\nsimple demonstrations of this law which are not based on\nthermodynamics; but thermodynamics, which led to its discovery,\ncontinues to give it its true scope. Moreover, it would not suffice\nmerely to determine quantitatively those laws of which it makes known\nthe general form. We must, if we wish to penetrate deeper into\ndetails, particularize the hypothesis, and admit, for instance, with\nGibbs that we are dealing with perfect gases; while, thanks to\nthermodynamics, we can constitute a complete theory of dissociation\nwhich leads to formulas in complete accord with the numerical results\nof the experiment. We can thus follow closely all questions concerning\nthe displacements of the equilibrium, and find a relation of the first\nimportance between the masses of the bodies which react in order to\nconstitute a system in equilibrium.\n\nThe statics thus constructed constitutes at the present day an\nimportant edifice to be henceforth classed amongst historical\nmonuments. Some theorists even wish to go a step beyond. They have\nattempted to begin by the same means a more complete study of those\nsystems whose state changes from one moment to another. This is,\nmoreover, a study which is necessary to complete satisfactorily the\nstudy of equilibrium itself; for without it grave doubts would exist\nas to the conditions of stability, and it alone can give their true\nmeaning to questions relating to displacements of equilibrium.\n\nThe problems with which we are thus confronted are singularly\ndifficult. M. Duhem has given us many excellent examples of the\nfecundity of the method; but if thermodynamic statics may be\nconsidered definitely founded, it cannot be said that the general\ndynamics of systems, considered as the study of thermal movements and\nvariations, are yet as solidly established.\n\n\nSec. 5. ATOMISM\n\nIt may appear singularly paradoxical that, in a chapter devoted to\ngeneral views on the principles of physics, a few words should be\nintroduced on the atomic theories of matter.\n\nVery often, in fact, what is called the physics of principles is set\nin opposition to the hypotheses on the constitution of matter,\nparticularly to atomic theories. I have already said that, abandoning\nthe investigation of the unfathomable mystery of the constitution of\nthe Universe, some physicists think they may find, in certain general\nprinciples, sufficient guides to conduct them across the physical\nworld. But I have also said, in examining the history of those\nprinciples, that if they are to-day considered experimental truths,\nindependent of all theories relating to matter, they have, in fact,\nnearly all been discovered by scholars who relied on molecular\nhypotheses: and the question suggests itself whether this is mere\nchance, or whether this chance may not be ordained by higher reasons.\n\nIn a very profound work which appeared a few years ago, entitled\n_Essai critique sur l'hypothese des atomes_, M. Hannequin, a\nphilosopher who is also an erudite scholar, examined the part taken by\natomism in the history of science. He notes that atomism and science\nwere born, in Greece, of the same problem, and that in modern times\nthe revival of the one was closely connected with that of the other.\nHe shows, too, by very close analysis, that the atomic hypothesis is\nessential to the optics of Fresnel and of Cauchy; that it penetrates\ninto the study of heat; and that, in its general features, it presided\nat the birth of modern chemistry and is linked with all its progress.\nHe concludes that it is, in a manner, the soul of our knowledge of\nNature, and that contemporary theories are on this point in accord\nwith history: for these theories consecrate the preponderance of this\nhypothesis in the domain of science.\n\nIf M. Hannequin had not been prematurely cut off in the full expansion\nof his vigorous talent, he might have added another chapter to his\nexcellent book. He would have witnessed a prodigious budding of\natomistic ideas, accompanied, it is true, by wide modifications in the\nmanner in which the atom is to be regarded, since the most recent\ntheories make material atoms into centres constituted of atoms of\nelectricity. On the other hand, he would have found in the bursting\nforth of these new doctrines one more proof in support of his idea\nthat science is indissolubly bound to atomism.\n\nFrom the philosophical point of view, M. Hannequin, examining the\nreasons which may have called these links into being, arrives at the\nidea that they necessarily proceed from the constitution of our\nknowledge, or, perhaps, from that of Nature itself. Moreover, this\norigin, double in appearance, is single at bottom. Our minds could\nnot, in fact, detach and come out of themselves to grasp reality and\nthe absolute in Nature. According to the idea of Descartes, it is the\ndestiny of our minds only to take hold of and to understand that which\nproceeds from them.\n\nThus atomism, which is, perhaps, only an appearance containing even\nsome contradictions, is yet a well-founded appearance, since it\nconforms to the laws of our minds; and this hypothesis is, in a way,\nnecessary.\n\nWe may dispute the conclusions of M. Hannequin, but no one will refuse\nto recognise, as he does, that atomic theories occupy a preponderating\npart in the doctrines of physics; and the position which they have\nthus conquered gives them, in a way, the right of saying that they\nrest on a real principle. It is in order to recognise this right that\nseveral physicists--M. Langevin, for example--ask that atoms be\npromoted from the rank of hypotheses to that of principles. By this\nthey mean that the atomistic ideas forced upon us by an almost\nobligatory induction based on very exact experiments, enable us to\nco-ordinate a considerable amount of facts, to construct a very general\nsynthesis, and to foresee a great number of phenomena.\n\nIt is of moment, moreover, to thoroughly understand that atomism does\nnot necessarily set up the hypothesis of centres of attraction acting\nat a distance, and it must not be confused with molecular physics,\nwhich has, on the other hand, undergone very serious checks. The\nmolecular physics greatly in favour some fifty years ago leads to such\ncomplex representations and to solutions often so undetermined, that\nthe most courageous are wearied with upholding it and it has fallen\ninto some discredit. It rested on the fundamental principles of\nmechanics applied to molecular actions; and that was, no doubt, an\nextension legitimate enough, since mechanics is itself only an\nexperimental science, and its principles, established for the\nmovements of matter taken as a whole, should not be applied outside\nthe domain which belongs to them. Atomism, in fact, tends more and\nmore, in modern theories, to imitate the principle of the conservation\nof energy or that of entropy, to disengage itself from the artificial\nbonds which attached it to mechanics, and to put itself forward as an\nindependent principle.\n\nAtomistic ideas also have undergone evolution, and this slow evolution\nhas been considerably quickened under the influence of modern\ndiscoveries. These reach back to the most remote antiquity, and to\nfollow their development we should have to write the history of human\nthought which they have always accompanied since the time of\nLeucippus, Democritus, Epicurus, and Lucretius. The first observers\nwho noticed that the volume of a body could be diminished by\ncompression or cold, or augmented by heat, and who saw a soluble solid\nbody mix completely with the water which dissolved it, must have been\ncompelled to suppose that matter was not dispersed continuously\nthroughout the space it seemed to occupy. They were thus brought to\nconsider it discontinuous, and to admit that a substance having the\nsame composition and the same properties in all its parts--in a word,\nperfectly homogeneous--ceases to present this homogeneity when\nconsidered within a sufficiently small volume.\n\nModern experimenters have succeeded by direct experiments in placing\nin evidence this heterogeneous character of matter when taken in small\nmass. Thus, for example, the superficial tension, which is constant\nfor the same liquid at a given temperature, no longer has the same\nvalue when the thickness of the layer of liquid becomes extremely\nsmall. Newton noticed even in his time that a dark zone is seen to\nform on a soap bubble at the moment when it becomes so thin that it\nmust burst. Professor Reinold and Sir Arthur Ruecker have shown that\nthis zone is no longer exactly spherical; and from this we must\nconclude that the superficial tension, constant for all thicknesses\nabove a certain limit, commences to vary when the thickness falls\nbelow a critical value, which these authors estimate, on optical\ngrounds, at about fifty millionths of a millimetre.\n\nFrom experiments on capillarity, Prof. Quincke has obtained similar\nresults with regard to layers of solids. But it is not only capillary\nproperties which allow this characteristic to be revealed. All the\nproperties of a body are modified when taken in small mass; M. Meslin\nproves this in a very ingenious way as regards optical properties, and\nMr Vincent in respect of electric conductivity. M. Houllevigue, who,\nin a chapter of his excellent work, _Du Laboratoire a l'Usine_, has\nvery clearly set forth the most interesting considerations on atomic\nhypotheses, has recently demonstrated that copper and silver cease to\ncombine with iodine as soon as they are present in a thickness of less\nthan thirty millionths of a millimetre. It is this same dimension\nlikewise that is possessed, according to M. Wiener, by the smallest\nthicknesses it is possible to deposit on glass. These layers are so\nthin that they cannot be perceived, but their presence is revealed by\na change in the properties of the light reflected by them.\n\nThus, below fifty to thirty millionths of a millimetre the properties\nof matter depend on its thickness. There are then, no doubt, only a\nfew molecules to be met with, and it may be concluded, in consequence,\nthat the discontinuous elements of bodies--that is, the molecules--\nhave linear dimensions of the order of magnitude of the millionth of a\nmillimetre. Considerations regarding more complex phenomena, for\ninstance the phenomena of electricity by contact, and also the kinetic\ntheory of gases, bring us to the same conclusion.\n\nThe idea of the discontinuity of matter forces itself upon us for many\nother reasons. All modern chemistry is founded on this principle; and\nlaws like the law of multiple proportions, introduce an evident\ndiscontinuity to which we find analogies in the law of electrolysis.\nThe elements of bodies we are thus brought to regard might, as regards\nsolids at all events, be considered as immobile; but this immobility\ncould not explain the phenomena of heat, and, as it is entirely\ninadmissible for gases, it seems very improbable it can absolutely\noccur in any state. We are thus led to suppose that these elements are\nanimated by very complicated movements, each one proceeding in closed\ntrajectories in which the least variations of temperature or pressure\ncause modifications.\n\nThe atomistic hypothesis shows itself remarkably fecund in the study\nof phenomena produced in gases, and here the mutual independence of\nthe particles renders the question relatively more simple and,\nperhaps, allows the principles of mechanics to be more certainly\nextended to the movements of molecules.\n\nThe kinetic theory of gases can point to unquestioned successes; and\nthe idea of Daniel Bernouilli, who, as early as 1738, considered a\ngaseous mass to be formed of a considerable number of molecules\nanimated by rapid movements of translation, has been put into a form\nprecise enough for mathematical analysis, and we have thus found\nourselves in a position to construct a really solid foundation. It\nwill be at once conceived, on this hypothesis, that pressure is the\nresultant of the shocks of the molecules against the walls of the\ncontaining vessel, and we at once come to the demonstration that the\nlaw of Mariotte is a natural consequence of this origin of pressure;\nsince, if the volume occupied by a certain number of molecules is\ndoubled, the number of shocks per second on each square centimetre of\nthe walls becomes half as much. But if we attempt to carry this\nfurther, we find ourselves in presence of a serious difficulty. It is\nimpossible to mentally follow every one of the many individual\nmolecules which compose even a very limited mass of gas. The path\nfollowed by this molecule may be every instant modified by the chance\nof running against another, or by a shock which may make it rebound in\nanother direction.\n\nThe difficulty would be insoluble if chance had not laws of its own.\nIt was Maxwell who first thought of introducing into the kinetic\ntheory the calculation of probabilities. Willard Gibbs and Boltzmann\nlater on developed this idea, and have founded a statistical method\nwhich does not, perhaps, give absolute certainty, but which is\ncertainly most interesting and curious. Molecules are grouped in such\na way that those belonging to the same group may be considered as\nhaving the same state of movement; then an examination is made of the\nnumber of molecules in each group, and what are the changes in this\nnumber from one moment to another. It is thus often possible to\ndetermine the part which the different groups have in the total\nproperties of the system and in the phenomena which may occur.\n\nSuch a method, analogous to the one employed by statisticians for\nfollowing the social phenomena in a population, is all the more\nlegitimate the greater the number of individuals counted in the\naverages; now, the number of molecules contained in a limited space--\nfor example, in a centimetre cube taken in normal conditions--is such\nthat no population could ever attain so high a figure. All\nconsiderations, those we have indicated as well as others which might\nbe invoked (for example, the recent researches of M. Spring on the\nlimit of visibility of fluorescence), give this result:--that there\nare, in this space, some twenty thousand millions of molecules. Each\nof these must receive in the space of a millimetre about ten thousand\nshocks, and be ten thousand times thrust out of its course. The free\npath of a molecule is then very small, but it can be singularly\naugmented by diminishing the number of them. Tait and Dewar have\ncalculated that, in a good modern vacuum, the length of the free path\nof the remaining molecules not taken away by the air-pump easily\nreaches a few centimetres.\n\nBy developing this theory, we come to consider that, for a given\ntemperature, every molecule (and even every individual particle, atom,\nor ion) which takes part in the movement has, on the average, the same\nkinetic energy in every body, and that this energy is proportional to\nthe absolute temperature; so that it is represented by this\ntemperature multiplied by a constant quantity which is a universal\nconstant.\n\nThis result is not an hypothesis but a very great probability. This\nprobability increases when it is noted that the same value for the\nconstant is met with in the study of very varied phenomena; for\nexample, in certain theories on radiation. Knowing the mass and energy\nof a molecule, it is easy to calculate its speed; and we find that the\naverage speed is about 400 metres per second for carbonic anhydride,\n500 for nitrogen, and 1850 for hydrogen at 0 deg. C. and at ordinary\npressure. I shall have occasion, later on, to speak of much more\nconsiderable speeds than these as animating other particles.\n\nThe kinetic theory has permitted the diffusion of gases to be\nexplained, and the divers circumstances of the phenomenon to be\ncalculated. It has allowed us to show, as M. Brillouin has done, that\nthe coefficient of diffusion of two gases does not depend on the\nproportion of the gases in the mixture; it gives a very striking image\nof the phenomena of viscosity and conductivity; and it leads us to\nthink that the coefficients of friction and of conductivity are\nindependent of the density; while all these previsions have been\nverified by experiment. It has also invaded optics; and by relying on\nthe principle of Doppler, Professor Michelson has succeeded in\nobtaining from it an explanation of the length presented by the\nspectral rays of even the most rarefied gases.\n\nBut however interesting are these results, they would not have\nsufficed to overcome the repugnance of certain physicists for\nspeculations which, an imposing mathematical baggage notwithstanding,\nseemed to them too hypothetical. The theory, moreover, stopped at the\nmolecule, and appeared to suggest no idea which could lead to the\ndiscovery of the key to the phenomena where molecules exercise a\nmutual influence on each other. The kinetic hypothesis, therefore,\nremained in some disfavour with a great number of persons,\nparticularly in France, until the last few years, when all the recent\ndiscoveries of the conductivity of gases and of the new radiations\ncame to procure for it a new and luxuriant efflorescence. It may be\nsaid that the atomistic synthesis, but yesterday so decried, is to-day\ntriumphant.\n\nThe elements which enter into the earlier kinetic theory, and which,\nto avoid confusion, should be always designated by the name of\nmolecules, were not, truth to say, in the eyes of the chemists, the\nfinal term of the divisibility of matter. It is well known that, to\nthem, except in certain particular bodies like the vapour of mercury\nand argon, the molecule comprises several atoms, and that, in compound\nbodies, the number of these atoms may even be fairly considerable. But\nphysicists rarely needed to have recourse to the consideration of\nthese atoms. They spoke of them to explain certain particularities of\nthe propagation of sound, and to enunciate laws relating to specific\nheats; but, in general, they stopped at the consideration of the\nmolecule.\n\nThe present theories carry the division much further. I shall not\ndwell now on these theories, since, in order to thoroughly understand\nthem, many other facts must be examined. But to avoid all confusion,\nit remains understood that, contrary, no doubt, to etymology, but in\nconformity with present custom, I shall continue in what follows to\ncall atoms those particles of matter which have till now been spoken\nof; these atoms being themselves, according to modern views,\nsingularly complex edifices formed of elements, of which we shall have\noccasion to indicate the nature later.\n\n\n\n\nCHAPTER IV\n\nTHE VARIOUS STATES OF MATTER\n\n\nSec. 1. THE STATICS OF FLUIDS\n\nThe division of bodies into gaseous, liquid, and solid, and the\ndistinction established for the same substance between the three\nstates, retain a great importance for the applications and usages of\ndaily life, but have long since lost their absolute value from the\nscientific point of view.\n\nSo far as concerns the liquid and gaseous states particularly, the\nalready antiquated researches of Andrews confirmed the ideas of\nCagniard de la Tour and established the continuity of the two states.\nA group of physical studies has thus been constituted on what may be\ncalled the statics of fluids, in which we examine the relations\nexisting between the pressure, the volume, and the temperature of\nbodies, and in which are comprised, under the term fluid, gases as\nwell as liquids.\n\nThese researches deserve attention by their interest and the\ngenerality of the results to which they have led. They also give a\nremarkable example of the happy effects which may be obtained by the\ncombined employment of the various methods of investigation used in\nexploring the domain of nature. Thermodynamics has, in fact, allowed\nus to obtain numerical relations between the various coefficients, and\natomic hypotheses have led to the establishment of one capital\nrelation, the characteristic equation of fluids; while, on the other\nhand, experiment in which the progress made in the art of measurement\nhas been utilized, has furnished the most valuable information on all\nthe laws of compressibility and dilatation.\n\nThe classical work of Andrews was not very wide. Andrews did not go\nmuch beyond pressures close to the normal and ordinary temperatures.\nOf late years several very interesting and peculiar cases have been\nexamined by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and\nother physicists. Sir W. Ramsay and Mr S. Young have made known the\nisothermal diagrams[6] of a certain number of liquid bodies at the\nordinary temperature. They have thus been able, while keeping to\nsomewhat restricted limits of temperature and pressure, to touch upon\nthe most important questions, since they found themselves in the\nregion of the saturation curve and of the critical point.\n\n[Footnote 6: By isothermal diagram is meant the pattern or complex\nformed when the isothermal lines are arranged in curves of which the\npressure is the ordinate and the volume the abscissa.--ED.]\n\nBut the most complete and systematic body of researches is due to M.\nAmagat, who undertook the study of a certain number of bodies, some\nliquid and some gaseous, extending the scope of his experiments so as\nto embrace the different phases of the phenomena and to compare\ntogether, not only the results relating to the same bodies, but also\nthose concerning different bodies which happen to be in the same\nconditions of temperature and pressure, but in very different\nconditions as regards their critical points.\n\nFrom the experimental point of view, M. Amagat has been able, with\nextreme skill, to conquer the most serious difficulties. He has\nmanaged to measure with precision pressures amounting to 3000\natmospheres, and also the very small volumes then occupied by the\nfluid mass under consideration. This last measurement, which\nnecessitates numerous corrections, is the most delicate part of the\noperation. These researches have dealt with a certain number of\ndifferent bodies. Those relating to carbonic acid and ethylene take in\nthe critical point. Others, on hydrogen and nitrogen, for instance,\nare very extended. Others, again, such as the study of the\ncompressibility of water, have a special interest, on account of the\npeculiar properties of this substance. M. Amagat, by a very concise\ndiscussion of the experiments, has also been able to definitely\nestablish the laws of compressibility and dilatation of fluids under\nconstant pressure, and to determine the value of the various\ncoefficients as well as their variations. It ought to be possible to\ncondense all these results into a single formula representing the\nvolume, the temperature, and the pressure. Rankin and, subsequently,\nRecknagel, and then Hirn, formerly proposed formulas of that kind; but\nthe most famous, the one which first appeared to contain in a\nsatisfactory manner all the facts which experiments brought to light\nand led to the production of many others, was the celebrated equation\nof Van der Waals.\n\nProfessor Van der Waals arrived at this relation by relying upon\nconsiderations derived from the kinetic theory of gases. If we keep to\nthe simple idea at the bottom of this theory, we at once demonstrate\nthat the gas ought to obey the laws of Mariotte and of Gay-Lussac, so\nthat the characteristic equation would be obtained by the statement\nthat the product of the number which is the measure of the volume by\nthat which is the measure of the pressure is equal to a constant\ncoefficient multiplied by the degree of the absolute temperature. But\nto get at this result we neglect two important factors.\n\nWe do not take into account, in fact, the attraction which the\nmolecules must exercise on each other. Now, this attraction, which is\nnever absolutely non-existent, may become considerable when the\nmolecules are drawn closer together; that is to say, when the\ncompressed gaseous mass occupies a more and more restricted volume. On\nthe other hand, we assimilate the molecules, as a first approximation,\nto material points without dimensions; in the evaluation of the path\ntraversed by each molecule no notice is taken of the fact that, at the\nmoment of the shock, their centres of gravity are still separated by a\ndistance equal to twice the radius of the molecule.\n\nM. Van der Waals has sought out the modifications which must be\nintroduced into the simple characteristic equation to bring it nearer\nto reality. He extends to the case of gases the considerations by\nwhich Laplace, in his famous theory of capillarity, reduced the effect\nof the molecular attraction to a perpendicular pressure exercised on\nthe surface of a liquid. This leads him to add to the external\npressure, that due to the reciprocal attractions of the gaseous\nparticles. On the other hand, when we attribute finite dimensions to\nthese particles, we must give a higher value to the number of shocks\nproduced in a given time, since the effect of these dimensions is to\ndiminish the mean path they traverse in the time which elapses between\ntwo consecutive shocks.\n\nThe calculation thus pursued leads to our adding to the pressure in\nthe simple equation a term which is designated the internal pressure,\nand which is the quotient of a constant by the square of the volume;\nalso to our deducting from the volume a constant which is the\nquadruple of the total and invariable volume which the gaseous\nmolecules would occupy did they touch one another.\n\nThe experiments fit in fairly well with the formula of Van der Waals,\nbut considerable discrepancies occur when we extend its limits,\nparticularly when the pressures throughout a rather wider interval are\nconsidered; so that other and rather more complex formulas, on which\nthere is no advantage in dwelling, have been proposed, and, in certain\ncases, better represent the facts.\n\nBut the most remarkable result of M. Van der Waals' calculations is\nthe discovery of corresponding states. For a long time physicists\nspoke of bodies taken in a comparable state. Dalton, for example,\npointed out that liquids have vapour-pressures equal to the\ntemperatures equally distant from their boiling-point; but that if, in\nthis particular property, liquids were comparable under these\nconditions of temperature, as regards other properties the parallelism\nwas no longer to be verified. No general rule was found until M. Van\nder Waals first enunciated a primary law, viz., that if the pressure,\nthe volume, and the temperature are estimated by taking as units the\ncritical quantities, the constants special to each body disappear in\nthe characteristic equation, which thus becomes the same for all\nfluids.\n\nThe words corresponding states thus take a perfectly precise\nsignification. Corresponding states are those for which the numerical\nvalues of the pressure, volume, and temperature, expressed by taking\nas units the values corresponding to the critical point, are equal;\nand, in corresponding states any two fluids have exactly the same\nproperties.\n\nM. Natanson, and subsequently P. Curie and M. Meslin, have shown by\nvarious considerations that the same result may be arrived at by\nchoosing units which correspond to any corresponding states; it has\nalso been shown that the theorem of corresponding states in no way\nimplies the exactitude of Van der Waals' formula. In reality, this is\nsimply due to the fact that the characteristic equation only contains\nthree constants.\n\nThe philosophical importance and the practical interest of the\ndiscovery nevertheless remain considerable. As was to be expected,\nnumbers of experimenters have sought whether these consequences are\nduly verified in reality. M. Amagat, particularly, has made use for\nthis purpose of a most original and simple method. He remarks that, in\nall its generality, the law may be translated thus: If the isothermal\ndiagrams of two substances be drawn to the same scale, taking as unit\nof volume and of pressure the values of the critical constants, the\ntwo diagrams should coincide; that is to say, their superposition\nshould present the aspect of one diagram appertaining to a single\nsubstance. Further, if we possess the diagrams of two bodies drawn to\nany scales and referable to any units whatever, as the changes of\nunits mean changes in the scale of the axes, we ought to make one of\nthe diagrams similar to the other by lengthening or shortening it in\nthe direction of one of the axes. M. Amagat then photographs two\nisothermal diagrams, leaving one fixed, but arranging the other so\nthat it may be free to turn round each axis of the co-ordinates; and\nby projecting, by means of a magic lantern, the second on the first,\nhe arrives in certain cases at an almost complete coincidence.\n\nThis mechanical means of proof thus dispenses with laborious\ncalculations, but its sensibility is unequally distributed over the\ndifferent regions of the diagram. M. Raveau has pointed out an equally\nsimple way of verifying the law, by remarking that if the logarithms\nof the pressure and volume are taken as co-ordinates, the co-ordinates\nof two corresponding points differ by two constant quantities, and the\ncorresponding curves are identical.\n\nFrom these comparisons, and from other important researches, among\nwhich should be particularly mentioned those of Mr S. Young and M.\nMathias, it results that the laws of corresponding states have not,\nunfortunately, the degree of generality which we at first attributed\nto them, but that they are satisfactory when applied to certain groups\nof bodies.[7]\n\n[Footnote 7: Mr Preston thus puts it: \"The law [of corresponding\nstates] seems to be not quite, but very nearly true for these\nsubstances [_i.e._ the halogen derivatives of benzene]; but in the\ncase of the other substances examined, the majority of these\ngeneralizations were either only roughly true or altogether departed\nfrom\" (_Theory of Heat_, London, 1904, p. 514.)--ED.]\n\nIf in the study of the statics of a simple fluid the experimental\nresults are already complex, we ought to expect much greater\ndifficulties when we come to deal with mixtures; still the problem has\nbeen approached, and many points are already cleared up.\n\nMixed fluids may first of all be regarded as composed of a large\nnumber of invariable particles. In this particularly simple case M.\nVan der Waals has established a characteristic equation of the\nmixtures which is founded on mechanical considerations. Various\nverifications of this formula have been effected, and it has, in\nparticular, been the object of very important remarks by M. Daniel\nBerthelot.\n\nIt is interesting to note that thermodynamics seems powerless to\ndetermine this equation, for it does not trouble itself about the\nnature of the bodies obedient to its laws; but, on the other hand, it\nintervenes to determine the properties of coexisting phases. If we\nexamine the conditions of equilibrium of a mixture which is not\nsubjected to external forces, it will be demonstrated that the\ndistribution must come back to a juxtaposition of homogeneous phases;\nin a given volume, matter ought so to arrange itself that the total\nsum of free energy has a minimum value. Thus, in order to elucidate\nall questions relating to the number and qualities of the phases into\nwhich the substance divides itself, we are led to regard the\ngeometrical surface which for a given temperature represents the free\nenergy.\n\nI am unable to enter here into the detail of the questions connected\nwith the theories of Gibbs, which have been the object of numerous\ntheoretical studies, and also of a series, ever more and more\nabundant, of experimental researches. M. Duhem, in particular, has\npublished, on the subject, memoirs of the highest importance, and a\ngreat number of experimenters, mostly scholars working in the physical\nlaboratory of Leyden under the guidance of the Director, Mr Kamerlingh\nOnnes, have endeavoured to verify the anticipations of the theory.\n\nWe are a little less advanced as regards abnormal substances; that is\nto say, those composed of molecules, partly simple and partly complex,\nand either dissociated or associated. These cases must naturally be\ngoverned by very complex laws. Recent researches by MM. Van der Waals,\nAlexeif, Rothmund, Kuenen, Lehfeld, etc., throw, however, some light on\nthe question.\n\nThe daily more numerous applications of the laws of corresponding\nstates have rendered highly important the determination of the\ncritical constants which permit these states to be defined. In the\ncase of homogeneous bodies the critical elements have a simple, clear,\nand precise sense; the critical temperature is that of the single\nisothermal line which presents a point of inflexion at a horizontal\ntangent; the critical pressure and the critical volume are the two\nco-ordinates of this point of inflexion.\n\nThe three critical constants may be determined, as Mr S. Young and M.\nAmagat have shown, by a direct method based on the consideration of\nthe saturated states. Results, perhaps more precise, may also be\nobtained if one keeps to two constants or even to a single one--\ntemperature, for example--by employing various special methods. Many\nothers, MM. Cailletet and Colardeau, M. Young, M.J. Chappuis, etc.,\nhave proceeded thus.\n\nThe case of mixtures is much more complicated. A binary mixture has a\ncritical space instead of a critical point. This space is comprised\nbetween two extreme temperatures, the lower corresponding to what is\ncalled the folding point, the higher to that which we call the point\nof contact of the mixture. Between these two temperatures an\nisothermal compression yields a quantity of liquid which increases,\nthen reaches a maximum, diminishes, and disappears. This is the\nphenomenon of retrograde condensation. We may say that the properties\nof the critical point of a homogeneous substance are, in a way,\ndivided, when it is a question of a binary mixture, between the two\npoints mentioned.\n\nCalculation has enabled M. Van der Waals, by the application of his\nkinetic theories, and M. Duhem, by means of thermodynamics, to foresee\nmost of the results which have since been verified by experiment. All\nthese facts have been admirably set forth and systematically\nco-ordinated by M. Mathias, who, by his own researches, moreover, has\nmade contributions of the highest value to the study of questions\nregarding the continuity of the liquid and gaseous states.\n\nThe further knowledge of critical elements has allowed the laws of\ncorresponding states to be more closely examined in the case of\nhomogeneous substances. It has shown that, as I have already said,\nbodies must be arranged in groups, and this fact clearly proves that\nthe properties of a given fluid are not determined by its critical\nconstants alone, and that it is necessary to add to them some other\nspecific parameters; M. Mathias and M. D. Berthelot have indicated\nsome which seem to play a considerable part.\n\nIt results also from this that the characteristic equation of a fluid\ncannot yet be considered perfectly known. Neither the equation of Van\nder Waals nor the more complicated formulas which have been proposed\nby various authors are in perfect conformity with reality. We may\nthink that researches of this kind will only be successful if\nattention is concentrated, not only on the phenomena of\ncompressibility and dilatation, but also on the calorimetric\nproperties of bodies. Thermodynamics indeed establishes relations\nbetween those properties and other constants, but does not allow\neverything to be foreseen.\n\nSeveral physicists have effected very interesting calorimetric\nmeasurements, either, like M. Perot, in order to verify Clapeyron's\nformula regarding the heat of vaporization, or to ascertain the values\nof specific heats and their variations when the temperature or the\npressure happens to change. M. Mathias has even succeeded in\ncompletely determining the specific heats of liquefied gases and of\ntheir saturated vapours, as well as the heat of internal and external\nvaporization.\n\n\nSec. 2. THE LIQUEFACTION OF GASES, AND THE PROPERTIES OF BODIES AT A\n     LOW TEMPERATURE\n\nThe scientific advantages of all these researches have been great,\nand, as nearly always happens, the practical consequences derived from\nthem have also been most important. It is owing to the more complete\nknowledge of the general properties of fluids that immense progress\nhas been made these last few years in the methods of liquefying gases.\n\nFrom a theoretical point of view the new processes of liquefaction can\nbe classed in two categories. Linde's machine and those resembling it\nutilize, as is known, expansion without any notable production of\nexternal work. This expansion, nevertheless, causes a fall in the\ntemperature, because the gas in the experiment is not a perfect gas,\nand, by an ingenious process, the refrigerations produced are made\ncumulative.\n\nSeveral physicists have proposed to employ a method whereby\nliquefaction should be obtained by expansion with recuperable external\nwork. This method, proposed as long ago as 1860 by Siemens, would\noffer considerable advantages. Theoretically, the liquefaction would\nbe more rapid, and obtained much more economically; but unfortunately\nin the experiment serious obstacles are met with, especially from the\ndifficulty of obtaining a suitable lubricant under intense cold for\nthose parts of the machine which have to be in movement if the\napparatus is to work.\n\nM. Claude has recently made great progress on this point by the use,\nduring the running of the machine, of the ether of petrol, which is\nuncongealable, and a good lubricant for the moving parts. When once\nthe desired region of cold is reached, air itself is used, which\nmoistens the metals but does not completely avoid friction; so that\nthe results would have remained only middling, had not this ingenious\nphysicist devised a new improvement which has some analogy with\nsuperheating of steam in steam engines. He slightly varies the initial\ntemperature of the compressed air on the verge of liquefaction so as\nto avoid a zone of deep perturbations in the properties of fluids,\nwhich would make the work of expansion very feeble and the cold\nproduced consequently slight. This improvement, simple as it is in\nappearance, presents several other advantages which immediately treble\nthe output.\n\nThe special object of M. Claude was to obtain oxygen in a practical\nmanner by the actual distillation of liquid air. Since nitrogen boils\nat -194 deg. and oxygen at -180.5 deg. C., if liquid air be evaporated, the\nnitrogen escapes, especially at the commencement of the evaporation,\nwhile the oxygen concentrates in the residual liquid, which finally\nconsists of pure oxygen, while at the same time the temperature rises\nto the boiling-point (-180.5 deg. C.) of oxygen. But liquid air is costly,\nand if one were content to evaporate it for the purpose of collecting\na part of the oxygen in the residuum, the process would have a very\npoor result from the commercial point of view. As early as 1892, Mr\nParkinson thought of improving the output by recovering the cold\nproduced by liquid air during its evaporation; but an incorrect idea,\nwhich seems to have resulted from certain experiments of Dewar--the\nidea that the phenomenon of the liquefaction of air would not be,\nowing to certain peculiarities, the exact converse of that of\nvaporization--led to the employment of very imperfect apparatus. M.\nClaude, however, by making use of a method which he calls the\nreversal[8] method, obtains a complete rectification in a remarkably\nsimple manner and under extremely advantageous economic conditions.\nApparatus, of surprisingly reduced dimensions but of great efficiency,\nis now in daily work, which easily enables more than a thousand cubic\nmetres of oxygen to be obtained at the rate, per horse-power, of more\nthan a cubic metre per hour.\n\n[Footnote 8: Methode avec retour en arriere.--ED]\n\nIt is in England, thanks to the skill of Sir James Dewar and his\npupils--thanks also, it must be said, to the generosity of the Royal\nInstitution, which has devoted considerable sums to these costly\nexperiments--that the most numerous and systematic researches have\nbeen effected on the production of intense cold. I shall here note\nonly the more important results, especially those relating to the\nproperties of bodies at low temperatures.\n\nTheir electrical properties, in particular, undergo some interesting\nmodifications. The order which metals assume in point of conductivity\nis no longer the same as at ordinary temperatures. Thus at -200 deg. C.\ncopper is a better conductor than silver. The resistance diminishes\nwith the temperature, and, down to about -200 deg., this diminution is\nalmost linear, and it would seem that the resistance tends towards\nzero when the temperature approaches the absolute zero. But, after\n-200 deg., the pattern of the curves changes, and it is easy to foresee\nthat at absolute zero the resistivities of all metals would still\nhave, contrary to what was formerly supposed, a notable value.\nSolidified electrolytes which, at temperatures far below their fusion\npoint, still retain a very appreciable conductivity, become, on the\ncontrary, perfect insulators at low temperatures. Their dielectric\nconstants assume relatively high values. MM. Curie and Compan, who\nhave studied this question from their own point of view, have noted,\nmoreover, that the specific inductive capacity changes considerably\nwith the temperature.\n\nIn the same way, magnetic properties have been studied. A very\ninteresting result is that found in oxygen: the magnetic\nsusceptibility of this body increases at the moment of liquefaction.\nNevertheless, this increase, which is enormous (since the\nsusceptibility becomes sixteen hundred times greater than it was at\nfirst), if we take it in connection with equal volumes, is much less\nconsiderable if taken in equal masses. It must be concluded from this\nfact that the magnetic properties apparently do not belong to the\nmolecules themselves, but depend on their state of aggregation.\n\nThe mechanical properties of bodies also undergo important\nmodifications. In general, their cohesion is greatly increased, and\nthe dilatation produced by slight changes of temperature is\nconsiderable. Sir James Dewar has effected careful measurements of the\ndilatation of certain bodies at low temperatures: for example, of ice.\nChanges in colour occur, and vermilion and iodide of mercury pass into\npale orange. Phosphorescence becomes more intense, and most bodies of\ncomplex structure--milk, eggs, feathers, cotton, and flowers--become\nphosphorescent. The same is the case with certain simple bodies, such\nas oxygen, which is transformed into ozone and emits a white light in\nthe process.\n\nChemical affinity is almost put an end to; phosphorus and potassium\nremain inert in liquid oxygen. It should, however, be noted, and this\nremark has doubtless some interest for the theories of photographic\naction, that photographic substances retain, even at the temperature\nof liquid hydrogen, a very considerable part of their sensitiveness to\nlight.\n\nSir James Dewar has made some important applications of low\ntemperatures in chemical analysis; he also utilizes them to create a\nvacuum. His researches have, in fact, proved that the pressure of air\ncongealed by liquid hydrogen cannot exceed the millionth of an\natmosphere. We have, then, in this process, an original and rapid\nmeans of creating an excellent vacuum in apparatus of very different\nkinds--a means which, in certain cases, may be particularly\nconvenient.[9]\n\n[Footnote 9: Professor Soddy, in a paper read before the Royal Society\non the 15th November 1906, warns experimenters against vacua created\nby charcoal cooled in liquid air (the method referred-to in the text),\nunless as much of the air as possible is first removed with a pump and\nreplaced by some argon-free gas. According to him, neither helium nor\nargon is absorbed by charcoal. By the use of electrically-heated\ncalcium, he claims to have produced an almost perfect vacuum.--ED.]\n\nThanks to these studies, a considerable field has been opened up for\nbiological research, but in this, which is not our subject, I shall\nnotice one point only. It has been proved that vital germs--bacteria,\nfor example--may be kept for seven days at -190 deg.C. without their\nvitality being modified. Phosphorescent organisms cease, it is true,\nto shine at the temperature of liquid air, but this fact is simply due\nto the oxidations and other chemical reactions which keep up the\nphosphorescence being then suspended, for phosphorescent activity\nreappears so soon as the temperature is again sufficiently raised. An\nimportant conclusion has been drawn from these experiments which\naffects cosmogonical theories: since the cold of space could not kill\nthe germs of life, it is in no way absurd to suppose that, under\nproper conditions, a germ may be transmitted from one planet to\nanother.\n\nAmong the discoveries made with the new processes, the one which most\nstrikingly interested public attention is that of new gases in the\natmosphere. We know how Sir William Ramsay and Dr. Travers first\nobserved by means of the spectroscope the characteristics of the\n_companions_ of argon in the least volatile part of the atmosphere.\nSir James Dewar on the one hand, and Sir William Ramsay on the other,\nsubsequently separated in addition to argon and helium, crypton,\nxenon, and neon. The process employed consists essentially in first\nsolidifying the least volatile part of the air and then causing it to\nevaporate with extreme slowness. A tube with electrodes enables the\nspectrum of the gas in process of distillation to be observed. In this\nmanner, the spectra of the various gases may be seen following one\nanother in the inverse order of their volatility. All these gases are\nmonoatomic, like mercury; that is to say, they are in the most simple\nstate, they possess no internal molecular energy (unless it is that\nwhich heat is capable of supplying), and they even seem to have no\nchemical energy. Everything leads to the belief that they show the\nexistence on the earth of an earlier state of things now vanished. It\nmay be supposed, for instance, that helium and neon, of which the\nmolecular mass is very slight, were formerly more abundant on our\nplanet; but at an epoch when the temperature of the globe was higher,\nthe very speed of their molecules may have reached a considerable\nvalue, exceeding, for instance, eleven kilometres per second, which\nsuffices to explain why they should have left our atmosphere. Crypton\nand neon, which have a density four times greater than oxygen, may, on\nthe contrary, have partly disappeared by solution at the bottom of the\nsea, where it is not absurd to suppose that considerable quantities\nwould be found liquefied at great depths.[10]\n\n[Footnote 10: Another view, viz. that these inert gases are a kind of\nwaste product of radioactive changes, is also gaining ground. The\ndiscovery of the radioactive mineral malacone, which gives off both\nhelium and argon, goes to support this. See Messrs Ketchin and\nWinterson's paper on the subject at the Chemical Society, 18th October\n1906.--ED.]\n\nIt is probable, moreover, that the higher regions of the atmosphere\nare not composed of the same air as that around us. Sir James Dewar\npoints out that Dalton's law demands that every gas composing the\natmosphere should have, at all heights and temperatures, the same\npressure as if it were alone, the pressure decreasing the less\nquickly, all things being equal, as its density becomes less. It\nresults from this that the temperature becoming gradually lower as we\nrise in the atmosphere, at a certain altitude there can no longer\nremain any traces of oxygen or nitrogen, which no doubt liquefy, and\nthe atmosphere must be almost exclusively composed of the most\nvolatile gases, including hydrogen, which M.A. Gautier has, like Lord\nRayleigh and Sir William Ramsay, proved to exist in the air. The\nspectrum of the _Aurora borealis_, in which are found the lines of\nthose parts of the atmosphere which cannot be liquefied in liquid\nhydrogen, together with the lines of argon, crypton, and xenon, is\nquite in conformity with this point of view. It is, however, singular\nthat it should be the spectrum of crypton, that is to say, of the\nheaviest gas of the group, which appears most clearly in the upper\nregions of the atmosphere.\n\nAmong the gases most difficult to liquefy, hydrogen has been the\nobject of particular research and of really quantitative experiments.\nIts properties in a liquid state are now very clearly known. Its\nboiling-point, measured with a helium thermometer which has been\ncompared with thermometers of oxygen and hydrogen, is -252 deg.; its\ncritical temperature is -241 deg. C.; its critical pressure, 15\natmospheres. It is four times lighter than water, it does not present\nany absorption spectrum, and its specific heat is the greatest known.\nIt is not a conductor of electricity. Solidified at 15 deg. absolute, it\nis far from reminding one by its aspect of a metal; it rather\nresembles a piece of perfectly pure ice, and Dr Travers attributes to\nit a crystalline structure. The last gas which has resisted\nliquefaction, helium, has recently been obtained in a liquid state; it\nappears to have its boiling-point in the neighbourhood of 6 deg.\nabsolute.[11]\n\n[Footnote 11: M. Poincare is here in error. Helium has never been\nliquefied.--ED.]\n\n\nSec. 3. SOLIDS AND LIQUIDS\n\nThe interest of the results to which the researches on the continuity\nbetween the liquid and the gaseous states have led is so great, that\nnumbers of scholars have naturally been induced to inquire whether\nsomething analogous might not be found in the case of liquids and\nsolids. We might think that a similar continuity ought to be there met\nwith, that the universal character of the properties of matter forbade\nall real discontinuity between two different states, and that, in\ntruth, the solid was a prolongation of the liquid state.\n\nTo discover whether this supposition is correct, it concerns us to\ncompare the properties of liquids and solids. If we find that all\nproperties are common to the two states we have the right to believe,\neven if they presented themselves in different degrees, that, by a\ncontinuous series of intermediary bodies, the two classes might yet be\nconnected. If, on the other hand, we discover that there exists in\nthese two classes some quality of a different nature, we must\nnecessarily conclude that there is a discontinuity which nothing can\nremove.\n\nThe distinction established, from the point of view of daily custom,\nbetween solids and liquids, proceeds especially from the difficulty\nthat we meet with in the one case, and the facility in the other, when\nwe wish to change their form temporarily or permanently by the action\nof mechanical force. This distinction only corresponds, however, in\nreality, to a difference in the value of certain coefficients. It is\nimpossible to discover by this means any absolute characteristic which\nestablishes a separation between the two classes. Modern researches\nprove this clearly. It is not without use, in order to well understand\nthem, to state precisely the meaning of a few terms generally rather\nloosely employed.\n\nIf a conjunction of forces acting on a homogeneous material mass\nhappens to deform it without compressing or dilating it, two very\ndistinct kinds of reactions may appear which oppose themselves to the\neffort exercised. During the time of deformation, and during that time\nonly, the first make their influence felt. They depend essentially on\nthe greater or less rapidity of the deformation, they cease with the\nmovement, and could not, in any case, bring the body back to its\npristine state of equilibrium. The existence of these reactions leads\nus to the idea of viscosity or internal friction.\n\nThe second kind of reactions are of a different nature. They continue\nto act when the deformation remains stationary, and, if the external\nforces happen to disappear, they are capable of causing the body to\nreturn to its initial form, provided a certain limit has not been\nexceeded. These last constitute rigidity.\n\nAt first sight a solid body appears to have a finite rigidity and an\ninfinite viscosity; a liquid, on the contrary, presents a certain\nviscosity, but no rigidity. But if we examine the matter more closely,\nbeginning either with the solids or with the liquids, we see this\ndistinction vanish.\n\nTresca showed long ago that internal friction is not infinite in a\nsolid; certain bodies can, so to speak, at once flow and be moulded.\nM.W. Spring has given many examples of such phenomena. On the other\nhand, viscosity in liquids is never non-existent; for were it so for\nwater, for example, in the celebrated experiment effected by Joule for\nthe determination of the mechanical equivalent of the caloric, the\nliquid borne along by the floats would slide without friction on the\nsurrounding liquid, and the work done by movement would be the same\nwhether the floats did or did not plunge into the liquid mass.\n\nIn certain cases observed long ago with what are called pasty bodies,\nthis viscosity attains a value almost comparable to that observed by\nM. Spring in some solids. Nor does rigidity allow us to establish a\nbarrier between the two states. Notwithstanding the extreme mobility\nof their particles, liquids contain, in fact, vestiges of the property\nwhich we formerly wished to consider the special characteristic of\nsolids.\n\nMaxwell before succeeded in rendering the existence of this rigidity\nvery probable by examining the optical properties of a deformed layer\nof liquid. But a Russian physicist, M. Schwedoff, has gone further,\nand has been able by direct experiments to show that a sheath of\nliquid set between two solid cylinders tends, when one of the\ncylinders is subjected to a slight rotation, to return to its original\nposition, and gives a measurable torsion to a thread upholding the\ncylinder. From the knowledge of this torsion the rigidity can be\ndeduced. In the case of a solution containing 1/2 per cent. of\ngelatine, it is found that this rigidity, enormous compared with that\nof water, is still, however, one trillion eight hundred and forty\nbillion times less than that of steel.\n\nThis figure, exact within a few billions, proves that the rigidity is\nvery slight, but exists; and that suffices for a characteristic\ndistinction to be founded on this property. In a general way, M.\nSpring has also established that we meet in solids, in a degree more\nor less marked, with the properties of liquids. When they are placed\nin suitable conditions of pressure and time, they flow through\norifices, transmit pressure in all directions, diffuse and dissolve\none into the other, and react chemically on each other. They may be\nsoldered together by compression; by the same means alloys may be\nproduced; and further, which seems to clearly prove that matter in a\nsolid state is not deprived of all molecular mobility, it is possible\nto realise suitable limited reactions and equilibria between solid\nsalts, and these equilibria obey the fundamental laws of\nthermodynamics.\n\nThus the definition of a solid cannot be drawn from its mechanical\nproperties. It cannot be said, after what we have just seen, that\nsolid bodies retain their form, nor that they have a limited\nelasticity, for M. Spring has made known a case where the elasticity\nof solids is without any limit.\n\nIt was thought that in the case of a different phenomenon--that of\ncrystallization--we might arrive at a clear distinction, because here\nwe should he dealing with a specific quality; and that crystallized\nbodies would be the true solids, amorphous bodies being at that time\nregarded as liquids viscous in the extreme.\n\nBut the studies of a German physicist, Professor O. Lehmann, seem to\nprove that even this means is not infallible. Professor Lehmann has\nsucceeded, in fact, in obtaining with certain organic compounds--\noleate of potassium, for instance--under certain conditions some\npeculiar states to which he has given the name of semi-fluid and\nliquid crystals. These singular phenomena can only be observed and\nstudied by means of a microscope, and the Carlsruhe Professor had to\ndevise an ingenious apparatus which enabled him to bring the\npreparation at the required temperature on to the very plate of the\nmicroscope.\n\nIt is thus made evident that these bodies act on polarized light in\nthe manner of a crystal. Those that M. Lehmann terms semi-liquid still\npresent traces of polyhedric delimitation, but with the peaks and\nangles rounded by surface-tension, while the others tend to a strictly\nspherical form. The optical examination of the first-named bodies is\nvery difficult, because appearances may be produced which are due to\nthe phenomena of refraction and imitate those of polarization. For the\nother kind, which are often as mobile as water, the fact that they\npolarize light is absolutely unquestionable.\n\nUnfortunately, all these liquids are turbid, and it may be objected\nthat they are not homogeneous. This want of homogeneity may, according\nto M. Quincke, be due to the existence of particles suspended in a\nliquid in contact with another liquid miscible with it and enveloping\nit as might a membrane, and the phenomena of polarization would thus\nbe quite naturally explained.[12]\n\n[Footnote 12: Professor Quincke's last hypothesis is that all liquids\non solidifying pass through a stage intermediate between solid and\nliquid, in which they form what he calls \"foam-cells,\" and assume a\nviscous structure resembling that of jelly. See _Proc. Roy. Soc. A._,\n23rd July 1906.--ED.]\n\nM. Tamman is of opinion that it is more a question of an emulsion,\nand, on this hypothesis, the action on light would actually be that\nwhich has been observed. Various experimenters have endeavoured of\nrecent years to elucidate this question. It cannot be considered\nabsolutely settled, but these very curious experiments, pursued with\ngreat patience and remarkable ingenuity, allow us to think that there\nreally exist certain intermediary forms between crystals and liquids\nin which bodies still retain a peculiar structure, and consequently\nact on light, but nevertheless possess considerable plasticity.\n\nLet us note that the question of the continuity of the liquid and\nsolid states is not quite the same as the question of knowing whether\nthere exist bodies intermediate in all respects between the solids and\nliquids. These two problems are often wrongly confused. The gap\nbetween the two classes of bodies may be filled by certain substances\nwith intermediate properties, such as pasty bodies and bodies liquid\nbut still crystallized, because they have not yet completely lost\ntheir peculiar structure. Yet the transition is not necessarily\nestablished in a continuous fashion when we are dealing with the\npassage of one and the same determinate substance from the liquid to\nthe solid form. We conceive that this change may take place by\ninsensible degrees in the case of an amorphous body. But it seems\nhardly possible to consider the case of a crystal, in which molecular\nmovements must be essentially regular, as a natural sequence to the\ncase of the liquid where we are, on the contrary, in presence of an\nextremely disordered state of movement.\n\nM. Tamman has demonstrated that amorphous solids may very well, in\nfact, be regarded as superposed liquids endowed with very great\nviscosity. But it is no longer the same thing when the solid is once\nin the crystallized state. There is then a solution of continuity of\nthe various properties of the substance, and the two phases may\nco-exist.\n\nWe might presume also, by analogy with what happens with liquids and\ngases, that if we followed the curve of transformation of the\ncrystalline into the liquid phase, we might arrive at a kind of\ncritical point at which the discontinuity of their properties would\nvanish.\n\nProfessor Poynting, and after him Professor Planck and Professor\nOstwald, supposed this to be the case, but more recently M. Tamman has\nshown that such a point does not exist, and that the region of\nstability of the crystallized state is limited on all sides. All along\nthe curve of transformation the two states may exist in equilibrium,\nbut we may assert that it is impossible to realize a continuous series\nof intermediaries between these two states. There will always be a\nmore or less marked discontinuity in some of the properties.\n\nIn the course of his researches M. Tamman has been led to certain very\nimportant observations, and has met with fresh allotropic\nmodifications in nearly all substances, which singularly complicate\nthe question. In the case of water, for instance, he finds that\nordinary ice transforms itself, under a given pressure, at the\ntemperature of -80 deg. C. into another crystalline variety which is\ndenser than water.\n\nThe statics of solids under high pressure is as yet, therefore, hardly\ndrafted, but it seems to promise results which will not be identical\nwith those obtained for the statics of fluids, though it will present\nat least an equal interest.\n\n\nSec. 4. THE DEFORMATIONS OF SOLIDS\n\nIf the mechanical properties of the bodies intermediate between solids\nand liquids have only lately been the object of systematic studies,\nadmittedly solid substances have been studied for a long time. Yet,\nnotwithstanding the abundance of researches published on elasticity by\ntheorists and experimenters, numerous questions with regard to them\nstill remain in suspense.\n\nWe only propose to briefly indicate here a few problems recently\nexamined, without going into the details of questions which belong\nmore to the domain of mechanics than to that of pure physics.\n\nThe deformations produced in solid bodies by increasing efforts\narrange themselves in two distinct periods. If the efforts are weak,\nthe deformations produced are also very weak and disappear when the\neffort ceases. They are then termed elastic. If the efforts exceed a\ncertain value, a part only of these deformations disappear, and a part\nare permanent.\n\nThe purity of the note emitted by a sound has been often invoked as a\nproof of the perfect isochronism of the oscillation, and,\nconsequently, as a demonstration _a posteriori_ of the correctness of\nthe early law of Hoocke governing elastic deformations. This law has,\nhowever, during some years been frequently disputed. Certain\nmechanicians or physicists freely admit it to be incorrect, especially\nas regards extremely weak deformations. According to a theory in some\nfavour, especially in Germany, i.e. the theory of Bach, the law which\nconnects the elastic deformations with the efforts would be an\nexponential one. Recent experiments by Professors Kohlrausch and\nGruncisen, executed under varied and precise conditions on brass, cast\niron, slate, and wrought iron, do not appear to confirm Bach's law.\nNothing, in point of fact, authorises the rejection of the law of\nHoocke, which presents itself as the most natural and most simple\napproximation to reality.\n\nThe phenomena of permanent deformation are very complex, and it\ncertainly seems that they cannot be explained by the older theories\nwhich insisted that the molecules only acted along the straight line\nwhich joined their centres. It becomes necessary, then, to construct\nmore complete hypotheses, as the MM. Cosserat have done in some\nexcellent memoirs, and we may then succeed in grouping together the\nfacts resulting from new experiments. Among the experiments of which\nevery theory must take account may be mentioned those by which Colonel\nHartmann has placed in evidence the importance of the lines which are\nproduced on the surface of metals when the limit of elasticity is\nexceeded.\n\nIt is to questions of the same order that the minute and patient\nresearches of M. Bouasse have been directed. This physicist, as\ningenious as he is profound, has pursued for several years experiments\non the most delicate points relating to the theory of elasticity, and\nhe has succeeded in defining with a precision not always attained even\nin the best esteemed works, the deformations to which a body must be\nsubjected in order to obtain comparable experiments. With regard to\nthe slight oscillations of torsion which he has specially studied, M.\nBouasse arrives at the conclusion, in an acute discussion, that we\nhardly know anything more than was proclaimed a hundred years ago by\nCoulomb. We see, by this example, that admirable as is the progress\naccomplished in certain regions of physics, there still exist many\nover-neglected regions which remain in painful darkness. The skill\nshown by M. Bouasse authorises us to hope that, thanks to his\nresearches, a strong light will some day illumine these unknown\ncorners.\n\nA particularly interesting chapter on elasticity is that relating to\nthe study of crystals; and in the last few years it has been the\nobject of remarkable researches on the part of M. Voigt. These\nresearches have permitted a few controversial questions between\ntheorists and experimenters to be solved: in particular, M. Voigt has\nverified the consequences of the calculations, taking care not to\nmake, like Cauchy and Poisson, the hypothesis of central forces a mere\nfunction of distance, and has recognized a potential which depends on\nthe relative orientation of the molecules. These considerations also\napply to quasi-isotropic bodies which are, in fact, networks of\ncrystals.\n\nCertain occasional deformations which are produced and disappear\nslowly may be considered as intermediate between elastic and permanent\ndeformations. Of these, the thermal deformation of glass which\nmanifests itself by the displacement of the zero of a thermometer is\nan example. So also the modifications which the phenomena of magnetic\nhysteresis or the variations of resistivity have just demonstrated.\n\nMany theorists have taken in hand these difficult questions. M.\nBrillouin endeavours to interpret these various phenomena by the\nmolecular hypothesis. The attempt may seem bold, since these phenomena\nare, for the most part, essentially irreversible, and seem,\nconsequently, not adaptable to mechanics. But M. Brillouin makes a\npoint of showing that, under certain conditions, irreversible\nphenomena may be created between two material points, the actions of\nwhich depend solely on their distance; and he furnishes striking\ninstances which appear to prove that a great number of irreversible\nphysical and chemical phenomena may be ascribed to the existence of\nstates of unstable equilibria.\n\nM. Duhem has approached the problem from another side, and endeavours\nto bring it within the range of thermodynamics. Yet ordinary\nthermodynamics could not account for experimentally realizable states\nof equilibrium in the phenomena of viscosity and friction, since this\nscience declares them to be impossible. M. Duhem, however, arrives at\nthe idea that the establishment of the equations of thermodynamics\npresupposes, among other hypotheses, one which is entirely arbitrary,\nnamely: that when the state of the system is given, external actions\ncapable of maintaining it in that state are determined without\nambiguity, by equations termed conditions of equilibrium of the\nsystem. If we reject this hypothesis, it will then be allowable to\nintroduce into thermodynamics laws previously excluded, and it will be\npossible to construct, as M. Duhem has done, a much more comprehensive\ntheory.\n\nThe ideas of M. Duhem have been illustrated by remarkable experimental\nwork. M. Marchis, for example, guided by these ideas, has studied the\npermanent modifications produced in glass by an oscillation of\ntemperature. These modifications, which may be called phenomena of the\nhysteresis of dilatation, may be followed in very appreciable fashion\nby means of a glass thermometer. The general results are quite in\naccord with the previsions of M. Duhem. M. Lenoble in researches on\nthe traction of metallic wires, and M. Chevalier in experiments on the\npermanent variations of the electrical resistance of wires of an alloy\nof platinum and silver when submitted to periodical variations of\ntemperature, have likewise afforded verifications of the theory\npropounded by M. Duhem.\n\nIn this theory, the representative system is considered dependent on\nthe temperature of one or several other variables, such as, for\nexample, a chemical variable. A similar idea has been developed in a\nvery fine set of memoirs on nickel steel, by M. Ch. Ed. Guillaume. The\neminent physicist, who, by his earlier researches, has greatly\ncontributed to the light thrown on the analogous question of the\ndisplacement of the zero in thermometers, concludes, from fresh\nresearches, that the residual phenomena are due to chemical\nvariations, and that the return to the primary chemical state causes\nthe variation to disappear. He applies his ideas not only to the\nphenomena presented by irreversible steels, but also to very different\nfacts; for example, to phosphorescence, certain particularities of\nwhich may be interpreted in an analogous manner.\n\nNickel steels present the most curious properties, and I have already\npointed out the paramount importance of one of them, hardly capable of\nperceptible dilatation, for its application to metrology and\nchronometry.[13] Others, also discovered by M. Guillaume in the course\nof studies conducted with rare success and remarkable ingenuity, may\nrender great services, because it is possible to regulate, so to\nspeak, at will their mechanical or magnetic properties.\n\n[Footnote 13: The metal known as \"invar.\"--ED.]\n\nThe study of alloys in general is, moreover, one of those in which the\nintroduction of the methods of physics has produced the greatest\neffects. By the microscopic examination of a polished surface or of\none indented by a reagent, by the determination of the electromotive\nforce of elements of which an alloy forms one of the poles, and by the\nmeasurement of the resistivities, the densities, and the differences\nof potential or contact, the most valuable indications as to their\nconstitution are obtained. M. Le Chatelier, M. Charpy, M. Dumas, M.\nOsmond, in France; Sir W. Roberts Austen and Mr. Stansfield, in\nEngland, have given manifold examples of the fertility of these\nmethods. The question, moreover, has had a new light thrown upon it by\nthe application of the principles of thermodynamics and of the phase\nrule.\n\nAlloys are generally known in the two states of solid and liquid.\nFused alloys consist of one or several solutions of the component\nmetals and of a certain number of definite combinations. Their\ncomposition may thus be very complex: but Gibbs' rule gives us at once\nimportant information on the point, since it indicates that there\ncannot exist, in general, more than two distinct solutions in an alloy\nof two metals.\n\nSolid alloys may be classed like liquid ones. Two metals or more\ndissolve one into the other, and form a solid solution quite analogous\nto the liquid solution. But the study of these solid solutions is\nrendered singularly difficult by the fact that the equilibrium so\nrapidly reached in the case of liquids in this case takes days and, in\ncertain cases, perhaps even centuries to become established.\n\n\n\n\nCHAPTER V\n\nSOLUTIONS AND ELECTROLYTIC DISSOCIATION\n\n\nSec. 1. SOLUTION\n\nVaporization and fusion are not the only means by which the physical\nstate of a body may be changed without modifying its chemical\nconstitution. From the most remote periods solution has also been\nknown and studied, but only in the last twenty years have we obtained\nother than empirical information regarding this phenomenon.\n\nIt is natural to employ here also the methods which have allowed us to\npenetrate into the knowledge of other transformations. The problem of\nsolution may be approached by way of thermodynamics and of the\nhypotheses of kinetics.\n\nAs long ago as 1858, Kirchhoff, by attributing to saline solutions--\nthat is to say, to mixtures of water and a non-volatile liquid like\nsulphuric acid--the properties of internal energy, discovered a\nrelation between the quantity of heat given out on the addition of a\ncertain quantity of water to a solution and the variations to which\ncondensation and temperature subject the vapour-tension of the\nsolution. He calculated for this purpose the variations of energy\nwhich are produced when passing from one state to another by two\ndifferent series of transformations; and, by comparing the two\nexpressions thus obtained, he established a relation between the\nvarious elements of the phenomenon. But, for a long time afterwards,\nthe question made little progress, because there seemed to be hardly\nany means of introducing into this study the second principle of\nthermodynamics.[14] It was the memoir of Gibbs which at last opened\nout this rich domain and enabled it to be rationally exploited. As\nearly as 1886, M. Duhem showed that the theory of the thermodynamic\npotential furnished precise information on solutions or liquid\nmixtures. He thus discovered over again the famous law on the lowering\nof the congelation temperature of solvents which had just been\nestablished by M. Raoult after a long series of now classic\nresearches.\n\n[Footnote 14: The \"second principle\" referred to has been thus\nenunciated: \"In every engine that produces work there is a fall of\ntemperature, and the maximum output of a perfect engine--_i.e._ the\nratio between the heat consumed in work and the heat supplied--depends\nonly on the extreme temperatures between which the fluid is\nevolved.\"--Demanet, _Notes de Physique Experimentale_, Louvain, 1905,\nfasc. 2, p. 147. Clausius put it in a negative form, as thus: No\nengine can of itself, without the aid of external agency, transfer\nheat from a body at low temperature to a body at a high temperature.\nCf. Ganot's _Physics_, 17th English edition, Sec. 508.--ED.]\n\nIn the minds of many persons, however, grave doubts persisted.\nSolution appeared to be an essentially irreversible phenomenon. It was\ntherefore, in all strictness, impossible to calculate the entropy of a\nsolution, and consequently to be certain of the value of the\nthermodynamic potential. The objection would be serious even to-day,\nand, in calculations, what is called the paradox of Gibbs would be an\nobstacle.\n\nWe should not hesitate, however, to apply the Phase Law to solutions,\nand this law already gives us the key to a certain number of facts. It\nputs in evidence, for example, the part played by the eutectic point--\nthat is to say, the point at which (to keep to the simple case in\nwhich we have to do with two bodies only, the solvent and the solute)\nthe solution is in equilibrium at once with the two possible solids,\nthe dissolved body and the solvent solidified. The knowledge of this\npoint explains the properties of refrigerating mixtures, and it is\nalso one of the most useful for the theory of alloys. The scruples of\nphysicists ought to have been removed on the memorable occasion when\nProfessor Van t'Hoff demonstrated that solution can operate reversibly\nby reason of the phenomena of osmosis. But the experiment can only\nsucceed in very rare cases; and, on the other hand, Professor Van\nt'Hoff was naturally led to another very bold conception. He regarded\nthe molecule of the dissolved body as a gaseous one, and assimilated\nsolution, not as had hitherto been the rule, to fusion, but to a kind\nof vaporization. Naturally his ideas were not immediately accepted by\nthe scholars most closely identified with the classic tradition. It\nmay perhaps not be without use to examine here the principles of\nProfessor Van t'Hoff's theory.\n\n\nSec. 2. OSMOSIS\n\nOsmosis, or diffusion through a septum, is a phenomenon which has been\nknown for some time. The discovery of it is attributed to the Abbe\nNollet, who is supposed to have observed it in 1748, during some\n\"researches on liquids in ebullition.\" A classic experiment by\nDutrochet, effected about 1830, makes this phenomenon clear. Into pure\nwater is plunged the lower part of a vertical tube containing pure\nalcohol, open at the top and closed at the bottom by a membrane, such\nas a pig's bladder, without any visible perforation. In a very short\ntime it will be found, by means of an areometer for instance, that the\nwater outside contains alcohol, while the alcohol of the tube, pure at\nfirst, is now diluted. Two currents have therefore passed through the\nmembrane, one of water from the outside to the inside, and one of\nalcohol in the converse direction. It is also noted that a difference\nin the levels has occurred, and that the liquid in the tube now rises\nto a considerable height. It must therefore be admitted that the flow\nof the water has been more rapid than that of the alcohol. At the\ncommencement, the water must have penetrated into the tube much more\nrapidly than the alcohol left it. Hence the difference in the levels,\nand, consequently, a difference of pressure on the two faces of the\nmembrane. This difference goes on increasing, reaches a maximum, then\ndiminishes, and vanishes when the diffusion is complete, final\nequilibrium being then attained.\n\nThe phenomenon is evidently connected with diffusion. If water is very\ncarefully poured on to alcohol, the two layers, separate at first,\nmingle by degrees till a homogeneous substance is obtained. The\nbladder seems not to have prevented this diffusion from taking place,\nbut it seems to have shown itself more permeable to water than to\nalcohol. May it not therefore be supposed that there must exist\ndividing walls in which this difference of permeability becomes\ngreater and greater, which would be permeable to the solvent and\nabsolutely impermeable to the solute? If this be so, the phenomena of\nthese _semi-permeable_ walls, as they are termed, can be observed in\nparticularly simple conditions.\n\nThe answer to this question has been furnished by biologists, at which\nwe cannot be surprised. The phenomena of osmosis are naturally of the\nfirst importance in the action of organisms, and for a long time have\nattracted the attention of naturalists. De Vries imagined that the\ncontractions noticed in the protoplasm of cells placed in saline\nsolutions were due to a phenomenon of osmosis, and, upon examining\nmore closely certain peculiarities of cell life, various scholars have\ndemonstrated that living cells are enclosed in membranes permeable to\ncertain substances and entirely impermeable to others. It was\ninteresting to try to reproduce artificially semi-permeable walls\nanalogous to those thus met with in nature;[15] and Traube and Pfeffer\nseem to have succeeded in one particular case. Traube has pointed out\nthat the very delicate membrane of ferrocyanide of potassium which is\nobtained with some difficulty by exposing it to the reaction of\nsulphate of copper, is permeable to water, but will not permit the\npassage of the majority of salts. Pfeffer, by producing these walls in\nthe interstices of a porous porcelain, has succeeded in giving them\nsufficient rigidity to allow measurements to be made. It must be\nallowed that, unfortunately, no physicist or chemist has been as lucky\nas these two botanists; and the attempts to reproduce semi-permeable\nwalls completely answering to the definition, have never given but\nmediocre results. If, however, the experimental difficulty has not\nbeen overcome in an entirely satisfactory manner, it at least appears\nvery probable that such walls may nevertheless exist.[16]\n\n[Footnote 15: See next note.--ED.]\n\n[Footnote 16: M. Stephane Leduc, Professor of Biology of Nantes, has\nmade many experiments in this connection, and the artificial cells\nexhibited by him to the Association francaise pour l'avancement des\nSciences, at their meeting at Grenoble in 1904 and reproduced in their\n\"Actes,\" are particularly noteworthy.--ED.]\n\nNevertheless, in the case of gases, there exists an excellent example\nof a semi-permeable wall, and a partition of platinum brought to a\nhigher than red heat is, as shown by M. Villard in some ingenious\nexperiments, completely impermeable to air, and very permeable, on the\ncontrary, to hydrogen. It can also be experimentally demonstrated that\non taking two recipients separated by such a partition, and both\ncontaining nitrogen mixed with varying proportions of hydrogen, the\nlast-named gas will pass through the partition in such a way that the\nconcentration--that is to say, the mass of gas per unit of volume--\nwill become the same on both sides. Only then will equilibrium be\nestablished; and, at that moment, an excess of pressure will naturally\nbe produced in that recipient which, at the commencement, contained\nthe gas with the smallest quantity of hydrogen.\n\nThis experiment enables us to anticipate what will happen in a liquid\nmedium with semi-permeable partitions. Between two recipients, one\ncontaining pure water, the other, say, water with sugar in solution,\nseparated by one of these partitions, there will be produced merely a\nmovement of the pure towards the sugared water, and following this, an\nincrease of pressure on the side of the last. But this increase will\nnot be without limits. At a certain moment the pressure will cease to\nincrease and will remain at a fixed value which now has a given\ndirection. This is the osmotic pressure.\n\nPfeffer demonstrated that, for the same substance, the osmotic\npressure is proportional to the concentration, and consequently in\ninverse ratio to the volume occupied by a similar mass of the solute.\nHe gave figures from which it was easy, as Professor Van t'Hoff found,\nto draw the conclusion that, in a constant volume, the osmotic\npressure is proportional to the absolute temperature. De Vries,\nmoreover, by his remarks on living cells, extended the results which\nPfeffer had applied to one case only--that is, to the one that he had\nbeen able to examine experimentally.\n\nSuch are the essential facts of osmosis. We may seek to interpret them\nand to thoroughly examine the mechanism of the phenomenon; but it must\nbe acknowledged that as regards this point, physicists are not\nentirely in accord. In the opinion of Professor Nernst, the\npermeability of semi-permeable membranes is simply due to differences\nof solubility in one of the substances of the membrane itself. Other\nphysicists think it attributable, either to the difference in the\ndimensions of the molecules, of which some might pass through the\npores of the membrane and others be stopped by their relative size, or\nto these molecules' greater or less mobility. For others, again, it is\nthe capillary phenomena which here act a preponderating part.\n\nThis last idea is already an old one: Jager, More, and Professor\nTraube have all endeavoured to show that the direction and speed of\nosmosis are determined by differences in the surface-tensions; and\nrecent experiments, especially those of Batelli, seem to prove that\nosmosis establishes itself in the way which best equalizes the\nsurface-tensions of the liquids on both sides of the partition.\nSolutions possessing the same surface-tension, though not in molecular\nequilibrium, would thus be always in osmotic equilibrium. We must not\nconceal from ourselves that this result would be in contradiction with\nthe kinetic theory.\n\n\nSec. 3. APPLICATION TO THE THEORY OF SOLUTION\n\nIf there really exist partitions permeable to one body and impermeable\nto another, it may be imagined that the homogeneous mixture of these\ntwo bodies might be effected in the converse way. It can be easily\nconceived, in fact, that by the aid of osmotic pressure it would be\npossible, for example, to dilute or concentrate a solution by driving\nthrough the partition in one direction or another a certain quantity\nof the solvent by means of a pressure kept equal to the osmotic\npressure. This is the important fact which Professor Van t' Hoff\nperceived. The existence of such a wall in all possible cases\nevidently remains only a very legitimate hypothesis,--a fact which\nought not to be concealed.\n\nRelying solely on this postulate, Professor Van t' Hoff easily\nestablished, by the most correct method, certain properties of the\nsolutions of gases in a volatile liquid, or of non-volatile bodies in\na volatile liquid. To state precisely the other relations, we must\nadmit, in addition, the experimental laws discovered by Pfeffer. But\nwithout any hypothesis it becomes possible to demonstrate the laws of\nRaoult on the lowering of the vapour-tension and of the freezing point\nof solutions, and also the ratio which connects the heat of fusion\nwith this decrease.\n\nThese considerable results can evidently be invoked as _a posteriori_\nproofs of the exactitude of the experimental laws of osmosis. They are\nnot, however, the only ones that Professor Van t' Hoff has obtained by\nthe same method. This illustrious scholar was thus able to find anew\nGuldberg and Waage's law on chemical equilibrium at a constant\ntemperature, and to show how the position of the equilibrium changes\nwhen the temperature happens to change.\n\nIf now we state, in conformity with the laws of Pfeffer, that the\nproduct of the osmotic pressure by the volume of the solution is equal\nto the absolute temperature multiplied by a coefficient, and then look\nfor the numerical figure of this latter in a solution of sugar, for\ninstance, we find that this value is the same as that of the analogous\ncoefficient of the characteristic equation of a perfect gas. There is\nin this a coincidence which has also been utilized in the preceding\nthermodynamic calculations. It may be purely fortuitous, but we can\nhardly refrain from finding in it a physical meaning.\n\nProfessor Van t'Hoff has considered this coincidence a demonstration\nthat there exists a strong analogy between a body in solution and a\ngas; as a matter of fact, it may seem that, in a solution, the\ndistance between the molecules becomes comparable to the molecular\ndistances met with in gases, and that the molecule acquires the same\ndegree of liberty and the same simplicity in both phenomena. In that\ncase it seems probable that solutions will be subject to laws\nindependent of the chemical nature of the dissolved molecule and\ncomparable to the laws governing gases, while if we adopt the kinetic\nimage for the gas, we shall be led to represent to ourselves in a\nsimilar way the phenomena which manifest themselves in a solution.\nOsmotic pressure will then appear to be due to the shock of the\ndissolved molecules against the membrane. It will come from one side\nof this partition to superpose itself on the hydrostatic pressure,\nwhich latter must have the same value on both sides.\n\nThe analogy with a perfect gas naturally becomes much greater as the\nsolution becomes more diluted. It then imitates gas in some other\nproperties; the internal work of the variation of volume is nil, and\nthe specific heat is only a function of the temperature. A solution\nwhich is diluted by a reversible method is cooled like a gas which\nexpands adiabatically.[17]\n\n[Footnote 17: That is, without receiving or emitting any heat.--ED.]\n\nIt must, however, be acknowledged that, in other points, the analogy\nis much less perfect. The opinion which sees in solution a phenomenon\nresembling fusion, and which has left an indelible trace in everyday\nlanguage (we shall always say: to melt sugar in water) is certainly\nnot without foundation. Certain of the reasons which might be invoked\nto uphold this opinion are too evident to be repeated here, though\nothers more recondite might be quoted. The fact that the internal\nenergy generally becomes independent of the concentration when the\ndilution reaches even a moderately high value is rather in favour of\nthe hypothesis of fusion.\n\nWe must not forget, however, the continuity of the liquid and gaseous\nstates; and we may consider it in an absolute way a question devoid of\nsense to ask whether in a solution the solute is in the liquid or the\ngaseous state. It is in the fluid state, and perhaps in conditions\nopposed to those of a body in the state of a perfect gas. It is known,\nof course, that in this case the manometrical pressure must be\nregarded as very great in relation to the internal pressure which, in\nthe characteristic equation, is added to the other. May it not seem\npossible that in the solution it is, on the contrary, the internal\npressure which is dominant, the manometric pressure becoming of no\naccount? The coincidence of the formulas would thus be verified, for\nall the characteristic equations are symmetrical with regard to these\ntwo pressures. From this point of view the osmotic pressure would be\nconsidered as the result of an attraction between the solvent and the\nsolute; and it would represent the difference between the internal\npressures of the solution and of the pure solvent. These hypotheses\nare highly interesting, and very suggestive; but from the way in which\nthe facts have been set forth, it will appear, no doubt, that there is\nno obligation to admit them in order to believe in the legitimacy of\nthe application of thermodynamics to the phenomena of solution.\n\n\nSec. 4. ELECTROLYTIC DISSOCIATION\n\nFrom the outset Professor Van t' Hoff was brought to acknowledge that\na great number of solutions formed very notable exceptions which were\nvery irregular in appearance. The analogy with gases did not seem to\nbe maintained, for the osmotic pressure had a very different value\nfrom that indicated by the theory. Everything, however, came right if\none multiplied by a factor, determined according to each case, but\ngreater than unity, the constant of the characteristic formula.\nSimilar divergences were manifested in the delays observed in\ncongelation, and disappeared when subjected to an analogous\ncorrection.\n\nThus the freezing-point of a normal solution, containing a molecule\ngramme (that is, the number of grammes equal to the figure\nrepresenting the molecular mass) of alcohol or sugar in water, falls\n1.85 deg. C. If the laws of solution were identically the same for a\nsolution of sea-salt, the same depression should be noticed in a\nsaline solution also containing 1 molecule per litre. In fact, the\nfall reaches 3.26 deg., and the solution behaves as if it contained, not\n1, but 1.75 normal molecules per litre. The consideration of the\nosmotic pressures would lead to similar observations, but we know that\nthe experiment would be more difficult and less precise.\n\nWe may wonder whether anything really analogous to this can be met with\nin the case of a gas, and we are thus led to consider the phenomena of\ndissociation.[18] If we heat a body which, in a gaseous state, is\ncapable of dissociation--hydriodic acid, for example--at a given\ntemperature, an equilibrium is established between three gaseous bodies,\nthe acid, the iodine, and the hydrogen. The total mass will follow with\nfair closeness Mariotte's law, but the characteristic constant will no\nlonger be the same as in the case of a non-dissociated gas. We here no\nlonger have to do with a single molecule, since each molecule is in part\ndissociated.\n\n[Footnote 18: Dissociation must be distinguished from decomposition,\nwhich is what occurs when the whole of a particle (compound, molecule,\natom, etc.) breaks up into its component parts. In dissociation the\nbreaking up is only partial, and the resultant consists of a mixture\nof decomposed and undecomposed parts. See Ganot's Physics, 17th\nEnglish edition, Sec. 395, for examples.--ED.]\n\nThe comparison of the two cases leads to the employment of a new image\nfor representing the phenomenon which has been produced throughout the\nsaline solution. We have introduced a single molecule of salt, and\neverything occurs as if there were 1.75 molecules. May it not really\nbe said that the number is 1.75, because the sea-salt is partly\ndissociated, and a molecule has become transformed into 0.75 molecule\nof sodium, 0.75 of chlorium, and 0.25 of salt?\n\nThis is a way of speaking which seems, at first sight, strangely\ncontradicted by experiment. Professor Van t' Hoff, like other\nchemists, would certainly have rejected--in fact, he did so at first--\nsuch a conception, if, about the same time, an illustrious Swedish\nscholar, M. Arrhenius, had not been brought to the same idea by\nanother road, and, had not by stating it precisely and modifying it,\npresented it in an acceptable form.\n\nA brief examination will easily show that all the substances which are\nexceptions to the laws of Van t'Hoff are precisely those which are\ncapable of conducting electricity when undergoing decomposition--that\nis to say, are electrolytes. The coincidence is absolute, and cannot\nbe simply due to chance.\n\nNow, the phenomena of electrolysis have, for a long time, forced upon\nus an almost necessary image. The saline molecule is always\ndecomposed, as we know, in the primary phenomenon of electrolysis into\ntwo elements which Faraday termed ions. Secondary reactions, no doubt,\noften come to complicate the question, but these are chemical\nreactions belonging to the general order of things, and have nothing\nto do with the electric action working on the solution. The simple\nphenomenon is always the same--decomposition into two ions, followed\nby the appearance of one of these ions at the positive and of the\nother at the negative electrode. But as the very slightest expenditure\nof energy is sufficient to produce the commencement of electrolysis,\nit is necessary to suppose that these two ions are not united by any\nforce. Thus the two ions are, in a way, dissociated. Clausius, who was\nthe first to represent the phenomena by this symbol, supposed, in\norder not to shock the feelings of chemists too much, that this\ndissociation only affected an infinitesimal fraction of the total\nnumber of the molecules of the salt, and thereby escaped all check.\n\nThis concession was unfortunate, and the hypothesis thus lost the\ngreater part of its usefulness. M. Arrhenius was bolder, and frankly\nrecognized that dissociation occurs at once in the case of a great\nnumber of molecules, and tends to increase more and more as the\nsolution becomes more dilute. It follows the comparison with a gas\nwhich, while partially dissociated in an enclosed space, becomes\nwholly so in an infinite one.\n\nM. Arrhenius was led to adopt this hypothesis by the examination of\nexperimental results relating to the conductivity of electrolytes. In\norder to interpret certain facts, it has to be recognized that a part\nonly of the molecules in a saline solution can be considered as\nconductors of electricity, and that by adding water the number of\nmolecular conductors is increased. This increase, too, though rapid at\nfirst, soon becomes slower, and approaches a certain limit which an\ninfinite dilution would enable it to attain. If the conducting\nmolecules are the dissociated molecules, then the dissociation (so\nlong as it is a question of strong acids and salts) tends to become\ncomplete in the case of an unlimited dilution.\n\nThe opposition of a large number of chemists and physicists to the\nideas of M. Arrhenius was at first very fierce. It must be noted with\nregret that, in France particularly, recourse was had to an arm which\nscholars often wield rather clumsily. They joked about these free ions\nin solution, and they asked to see this chlorine and this sodium which\nswam about the water in a state of liberty. But in science, as\nelsewhere, irony is not argument, and it soon had to be acknowledged\nthat the hypothesis of M. Arrhenius showed itself singularly fertile\nand had to be regarded, at all events, as a very expressive image, if\nnot, indeed, entirely in conformity with reality.\n\nIt would certainly be contrary to all experience, and even to common\nsense itself, to suppose that in dissolved chloride of sodium there is\nreally free sodium, if we suppose these atoms of sodium to be\nabsolutely identical with ordinary atoms. But there is a great\ndifference. In the one case the atoms are electrified, and carry a\nrelatively considerable positive charge, inseparable from their state\nas ions, while in the other they are in the neutral state. We may\nsuppose that the presence of this charge brings about modifications as\nextensive as one pleases in the chemical properties of the atom. Thus\nthe hypothesis will be removed from all discussion of a chemical\norder, since it will have been made plastic enough beforehand to adapt\nitself to all the known facts; and if we object that sodium cannot\nsubsist in water because it instantaneously decomposes the latter, the\nanswer is simply that the sodium ion does not decompose water as does\nordinary sodium.\n\nStill, other objections might be raised which could not be so easily\nrefuted. One, to which chemists not unreasonably attached great\nimportance, was this:--If a certain quantity of chloride of sodium is\ndissociated into chlorine and sodium, it should be possible, by\ndiffusion, for example, which brings out plainly the phenomena of\ndissociation in gases, to extract from the solution a part either of\nthe chlorine or of the sodium, while the corresponding part of the\nother compound would remain. This result would be in flagrant\ncontradiction with the fact that, everywhere and always, a solution of\nsalt contains strictly the same proportions of its component elements.\n\nM. Arrhenius answers to this that the electrical forces in ordinary\nconditions prevent separation by diffusion or by any other process.\nProfessor Nernst goes further, and has shown that the concentration\ncurrents which are produced when two electrodes of the same substance\nare plunged into two unequally concentrated solutions may be\ninterpreted by the hypothesis that, in these particular conditions,\nthe diffusion does bring about a separation of the ions. Thus the\nargument is turned round, and the proof supposed to be given of the\nincorrectness of the theory becomes a further reason in its favour.\n\nIt is possible, no doubt, to adduce a few other experiments which are\nnot very favourable to M. Arrhenius's point of view, but they are\nisolated cases; and, on the whole, his theory has enabled many\nisolated facts, till then scattered, to be co-ordinated, and has\nallowed very varied phenomena to be linked together. It has also\nsuggested--and, moreover, still daily suggests--researches of the\nhighest order.\n\nIn the first place, the theory of Arrhenius explains electrolysis very\nsimply. The ions which, so to speak, wander about haphazard, and are\nuniformly distributed throughout the liquid, steer a regular course as\nsoon as we dip in the trough containing the electrolyte the two\nelectrodes connected with the poles of the dynamo or generator of\nelectricity. Then the charged positive ions travel in the direction of\nthe electromotive force and the negative ions in the opposite\ndirection. On reaching the electrodes they yield up to them the\ncharges they carry, and thus pass from the state of ion into that of\nordinary atom. Moreover, for the solution to remain in equilibrium,\nthe vanished ions must be immediately replaced by others, and thus the\nstate of ionisation of the electrolyte remains constant and its\nconductivity persists.\n\nAll the peculiarities of electrolysis are capable of interpretation:\nthe phenomena of the transport of ions, the fine experiments of M.\nBouty, those of Professor Kohlrausch and of Professor Ostwald on\nvarious points in electrolytic conduction, all support the theory. The\nverifications of it can even be quantitative, and we can foresee\nnumerical relations between conductivity and other phenomena. The\nmeasurement of the conductivity permits the number of molecules\ndissociated in a given solution to be calculated, and the number is\nthus found to be precisely the same as that arrived at if it is wished\nto remove the disagreement between reality and the anticipations which\nresult from the theory of Professor Van t' Hoff. The laws of\ncryoscopy, of tonometry, and of osmosis thus again become strict, and\nno exception to them remains.\n\nIf the dissociation of salts is a reality and is complete in a dilute\nsolution, any of the properties of a saline solution whatever should\nbe represented numerically as the sum of three values, of which one\nconcerns the positive ion, a second the negative ion, and the third\nthe solvent. The properties of the solutions would then be what are\ncalled additive properties. Numerous verifications may be attempted by\nvery different roads. They generally succeed very well; and whether we\nmeasure the electric conductivity, the density, the specific heats,\nthe index of refraction, the power of rotatory polarization, the\ncolour, or the absorption spectrum, the additive property will\neverywhere be found in the solution.\n\nThe hypothesis, so contested at the outset by the chemists, is,\nmoreover, assuring its triumph by important conquests in the domain of\nchemistry itself. It permits us to give a vivid explanation of\nchemical reaction, and for the old motto of the chemists, \"Corpora non\nagunt, nisi soluta,\" it substitutes a modern one, \"It is especially\nthe ions which react.\" Thus, for example, all salts of iron, which\ncontain iron in the state of ions, give similar reactions; but salts\nsuch as ferrocyanide of potassium, in which iron does not play the\npart of an ion, never give the characteristic reactions of iron.\n\nProfessor Ostwald and his pupils have drawn from the hypothesis of\nArrhenius manifold consequences which have been the cause of\nconsiderable progress in physical chemistry. Professor Ostwald has\nshown, in particular, how this hypothesis permits the quantitative\ncalculation of the conditions of equilibrium of electrolytes and\nsolutions, and especially of the phenomena of neutralization. If a\ndissolved salt is partly dissociated into ions, this solution must be\nlimited by an equilibrium between the non-dissociated molecule and the\ntwo ions resulting from the dissociation; and, assimilating the\nphenomenon to the case of gases, we may take for its study the laws of\nGibbs and of Guldberg and Waage. The results are generally very\nsatisfactory, and new researches daily furnish new checks.\n\nProfessor Nernst, who before gave, as has been said, a remarkable\ninterpretation of the diffusion of electrolytes, has, in the direction\npointed out by M. Arrhenius, developed a theory of the entire\nphenomena of electrolysis, which, in particular, furnishes a striking\nexplanation of the mechanism of the production of electromotive force\nin galvanic batteries.\n\nExtending the analogy, already so happily invoked, between the\nphenomena met with in solutions and those produced in gases, Professor\nNernst supposes that metals tend, as it were, to vaporize when in\npresence of a liquid. A piece of zinc introduced, for example, into\npure water gives birth to a few metallic ions. These ions become\npositively charged, while the metal naturally takes an equal charge,\nbut of contrary sign. Thus the solution and the metal are both\nelectrified; but this sort of vaporization is hindered by\nelectrostatic attraction, and as the charges borne by the ions are\nconsiderable, an equilibrium will be established, although the number\nof ions which enter the solution will be very small.\n\nIf the liquid, instead of being a solvent like pure water, contains an\nelectrolyte, it already contains metallic ions, the osmotic pressure\nof which will be opposite to that of the solution. Three cases may\nthen present themselves--either there will be equilibrium, or the\nelectrostatic attraction will oppose itself to the pressure of\nsolution and the metal will be negatively charged, or, finally, the\nattraction will act in the same direction as the pressure, and the\nmetal will become positively and the solution negatively charged.\nDeveloping this idea, Professor Nernst calculates, by means of the\naction of the osmotic pressures, the variations of energy brought into\nplay and the value of the differences of potential by the contact of\nthe electrodes and electrolytes. He deduces this from the\nelectromotive force of a single battery cell which becomes thus\nconnected with the values of the osmotic pressures, or, if you will,\nthanks to the relation discovered by Van t' Hoff, with the\nconcentrations. Some particularly interesting electrical phenomena\nthus become connected with an already very important group, and a new\nbridge is built which unites two regions long considered foreign to\neach other.\n\nThe recent discoveries on the phenomena produced in gases when\nrendered conductors of electricity almost force upon us, as we shall\nsee, the idea that there exist in these gases electrified centres\nmoving through the field, and this idea gives still greater\nprobability to the analogous theory explaining the mechanism of the\nconductivity of liquids. It will also be useful, in order to avoid\nconfusion, to restate with precision this notion of electrolytic ions,\nand to ascertain their magnitude, charge, and velocity.\n\nThe two classic laws of Faraday will supply us with important\ninformation. The first indicates that the quantity of electricity\npassing through the liquid is proportional to the quantity of matter\ndeposited on the electrodes. This leads us at once to the\nconsideration that, in any given solution, all the ions possess\nindividual charges equal in absolute value.\n\nThe second law may be stated in these terms: an atom-gramme of metal\ncarries with it into electrolysis a quantity of electricity\nproportionate to its valency.[19]\n\n[Footnote 19: The valency or atomicity of an element may be defined as\nthe power it possesses of entering into compounds in a certain fixed\nproportion. As hydrogen is generally taken as the standard, in\npractice the valency of an atom is the number of hydrogen atoms it\nwill combine with or replace. Thus chlorine and the rest of the\nhalogens, the atoms of which combine with one atom of hydrogen, are\ncalled univalent, oxygen a bivalent element, and so on.--ED.]\n\nNumerous experiments have made known the total mass of hydrogen\ncapable of carrying one coulomb, and it will therefore be possible to\nestimate the charge of an ion of hydrogen if the number of atoms of\nhydrogen in a given mass be known. This last figure is already\nfurnished by considerations derived from the kinetic theory, and\nagrees with the one which can be deduced from the study of various\nphenomena. The result is that an ion of hydrogen having a mass of 1.3\nx 10^{-20} grammes bears a charge of 1.3 X 10^{-20} electromagnetic\nunits; and the second law will immediately enable the charge of any\nother ion to be similarly estimated.\n\nThe measurements of conductivity, joined to certain considerations\nrelating to the differences of concentration which appear round the\nelectrode in electrolysis, allow the speed of the ions to be\ncalculated. Thus, in a liquid containing 1/10th of a hydrogen-ion per\nlitre, the absolute speed of an ion would be 3/10ths of a millimetre\nper second in a field where the fall of potential would be 1 volt per\ncentimetre. Sir Oliver Lodge, who has made direct experiments to\nmeasure this speed, has obtained a figure very approximate to this.\nThis value is very small compared to that which we shall meet with in\ngases.\n\nAnother consequence of the laws of Faraday, to which, as early as 1881,\nHelmholtz drew attention, may be considered as the starting-point of\ncertain new doctrines we shall come across later.\n\nHelmholtz says: \"If we accept the hypothesis that simple bodies are\ncomposed of atoms, we are obliged to admit that, in the same way,\nelectricity, whether positive or negative, is composed of elementary\nparts which behave like atoms of electricity.\"\n\nThe second law seems, in fact, analogous to the law of multiple\nproportions in chemistry, and it shows us that the quantities of\nelectricity carried vary from the simple to the double or treble,\naccording as it is a question of a uni-, bi-, or trivalent metal; and\nas the chemical law leads up to the conception of the material atom,\nso does the electrolytic law suggest the idea of an electric atom.\n\n\n\n\nCHAPTER VI\n\nTHE ETHER\n\n\nSec. 1. THE LUMINIFEROUS ETHER\n\nIt is in the works of Descartes that we find the first idea of\nattributing those physical phenomena which the properties of matter\nfail to explain to some subtle matter which is the receptacle of the\nenergy of the universe.\n\nIn our times this idea has had extraordinary luck. After having been\neclipsed for two hundred years by the success of the immortal\nsynthesis of Newton, it gained an entirely new splendour with Fresnel\nand his followers. Thanks to their admirable discoveries, the first\nstage seemed accomplished, the laws of optics were represented by a\nsingle hypothesis, marvellously fitted to allow us to anticipate\nunknown phenomena, and all these anticipations were subsequently fully\nverified by experiment. But the researches of Faraday, Maxwell, and\nHertz authorized still greater ambitions; and it really seemed that\nthis medium, to which it was agreed to give the ancient name of ether,\nand which had already explained light and radiant heat, would also be\nsufficient to explain electricity. Thus the hope began to take form\nthat we might succeed in demonstrating the unity of all physical\nforces. It was thought that the knowledge of the laws relating to the\ninmost movements of this ether might give us the key to all phenomena,\nand might make us acquainted with the method in which energy is stored\nup, transmitted, and parcelled out in its external manifestations.\n\nWe cannot study here all the problems which are connected with the\nphysics of the ether. To do this a complete treatise on optics would\nhave to be written and a very lengthy one on electricity. I shall\nsimply endeavour to show rapidly how in the last few years the ideas\nrelative to the constitution of this ether have evolved, and we shall\nsee if it be possible without self-delusion to imagine that a single\nmedium can really allow us to group all the known facts in one\ncomprehensive arrangement.\n\nAs constructed by Fresnel, the hypothesis of the luminous ether, which\nhad so great a struggle at the outset to overcome the stubborn\nresistance of the partisans of the then classic theory of emission,\nseemed, on the contrary, to possess in the sequel an unshakable\nstrength. Lame, though a prudent mathematician, wrote: \"_The\nexistence_ of the ethereal fluid is _incontestably demonstrated_ by\nthe propagation of light through the planetary spaces, and by the\nexplanation, so simple and so complete, of the phenomena of\ndiffraction in the wave theory of light\"; and he adds: \"The laws of\ndouble refraction prove with no less certainty that the _ether exists_\nin all diaphanous media.\" Thus the ether was no longer an hypothesis,\nbut in some sort a tangible reality. But the ethereal fluid of which\nthe existence was thus proclaimed has some singular properties.\n\nWere it only a question of explaining rectilinear propagation,\nreflexion, refraction, diffraction, and interferences notwithstanding\ngrave difficulties at the outset and the objections formulated by\nLaplace and Poisson (some of which, though treated somewhat lightly at\nthe present day, have not lost all value), we should be under no\nobligation to make any hypothesis other than that of the undulations\nof an elastic medium, without deciding in advance anything as to the\nnature and direction of the vibrations.\n\nThis medium would, naturally--since it exists in what we call the\nvoid--be considered as imponderable. It may be compared to a fluid of\nnegligible mass--since it offers no appreciable resistance to the\nmotion of the planets--but is endowed with an enormous elasticity,\nbecause the velocity of the propagation of light is considerable. It\nmust be capable of penetrating into all transparent bodies, and of\nretaining there, so to speak, a constant elasticity, but must there\nbecome condensed, since the speed of propagation in these bodies is\nless than in a vacuum. Such properties belong to no material gas, even\nthe most rarefied, but they admit of no essential contradiction, and\nthat is the important point.[20]\n\n[Footnote 20: Since this was written, however, men of science have\nbecome less unanimous than they formerly were on this point. The\nveteran chemist Professor Mendeleeff has given reasons for thinking\nthat the ether is an inert gas with an atomic weight a million times\nless than that of hydrogen, and a velocity of 2250 kilometres per\nsecond (_Principles of Chemistry_, Eng. ed., 1905, vol. ii. p. 526).\nOn the other hand, the well-known physicist Dr A.H. Bucherer, speaking\nat the Naturforscherversammlung, held at Stuttgart in 1906, declared\nhis disbelief in the existence of the ether, which he thought could\nnot be reconciled at once with the Maxwellian theory and the known\nfacts.--ED.]\n\nIt was the study of the phenomena of polarization which led Fresnel to\nhis bold conception of transverse vibrations, and subsequently induced\nhim to penetrate further into the constitution of the ether. We know\nthe experiment of Arago on the noninterference of polarized rays in\nrectangular planes. While two systems of waves, proceeding from the\nsame source of natural light and propagating themselves in nearly\nparallel directions, increase or become destroyed according to whether\nthe nature of the superposed waves are of the same or of contrary\nsigns, the waves of the rays polarized in perpendicular planes, on the\nother hand, can never interfere with each other. Whatever the\ndifference of their course, the intensity of the light is always the\nsum of the intensity of the two rays.\n\nFresnel perceived that this experiment absolutely compels us to reject\nthe hypothesis of longitudinal vibrations acting along the line of\npropagation in the direction of the rays. To explain it, it must of\nnecessity be admitted, on the contrary, that the vibrations are\ntransverse and perpendicular to the ray. Verdet could say, in all\ntruth, \"It is not possible to deny the transverse direction of\nluminous vibrations, without at the same time denying that light\nconsists of an undulatory movement.\"\n\nSuch vibrations do not and cannot exist in any medium resembling a\nfluid. The characteristic of a fluid is that its different parts can\ndisplace themselves with regard to one another without any reaction\nappearing so long as a variation of volume is not produced. There\ncertainly may exist, as we have seen, certain traces of rigidity in a\nliquid, but we cannot conceive such a thing in a body infinitely more\nsubtle than rarefied gas. Among material bodies, a solid alone really\npossesses the rigidity sufficient for the production within it of\ntransverse vibrations and for their maintenance during their\npropagation.\n\nSince we have to attribute such a property to the ether, we may add\nthat on this point it resembles a solid, and Lord Kelvin has shown\nthat this solid, would be much more rigid than steel. This conclusion\nproduces great surprise in all who hear it for the first time, and it\nis not rare to hear it appealed to as an argument against the actual\nexistence of the ether. It does not seem, however, that such an\nargument can be decisive. There is no reason for supposing that the\nether ought to be a sort of extension of the bodies we are accustomed\nto handle. Its properties may astonish our ordinary way of thinking,\nbut this rather unscientific astonishment is not a reason for doubting\nits existence. Real difficulties would appear only if we were led to\nattribute to the ether, not singular properties which are seldom found\nunited in the same substance, but properties logically contradictory.\nIn short, however odd such a medium may appear to us, it cannot be\nsaid that there is any absolute incompatibility between its\nattributes.\n\nIt would even be possible, if we wished, to suggest images capable of\nrepresenting these contrary appearances. Various authors have done so.\nThus, M. Boussinesq assumes that the ether behaves like a very\nrarefied gas in respect of the celestial bodies, because these last\nmove, while bathed in it, in all directions and relatively slowly,\nwhile they permit it to retain, so to speak, its perfect homogeneity.\nOn the other hand, its own undulations are so rapid that so far as\nthey are concerned the conditions become very different, and its\nfluidity has, one might say, no longer the time to come in. Hence its\nrigidity alone appears.\n\nAnother consequence, very important in principle, of the fact that\nvibrations of light are transverse, has been well put in evidence by\nFresnel. He showed how we have, in order to understand the action\nwhich excites without condensation the sliding of successive layers of\nthe ether during the propagation of a vibration, to consider the\nvibrating medium as being composed of molecules separated by finite\ndistances. Certain authors, it is true, have proposed theories in\nwhich the action at a distance of these molecules are replaced by\nactions of contact between parallelepipeds sliding over one another;\nbut, at bottom, these two points of view both lead us to conceive the\nether as a discontinuous medium, like matter itself. The ideas\ngathered from the most recent experiments also bring us to the same\nconclusion.\n\n\nSec. 2. RADIATIONS\n\nIn the ether thus constituted there are therefore propagated\ntransverse vibrations, regarding which all experiments in optics\nfurnish very precise information. The amplitude of these vibrations is\nexceedingly small, even in relation to the wave-length, small as these\nlast are. If, in fact, the amplitude of the vibrations acquired a\nnoticeable value in comparison with the wave-length, the speed of\npropagation should increase with the amplitude. Yet, in spite of some\ncurious experiments which seem to establish that the speed of light\ndoes alter a little with its intensity, we have reason to believe\nthat, as regards light, the amplitude of the oscillations in relation\nto the wave-length is incomparably less than in the case of sound.\n\nIt has become the custom to characterise each vibration by the path\nwhich the vibratory movement traverses during the space of a\nvibration--by the length of wave, in a word--rather than by the\nduration of the vibration itself. To measure wave-lengths, the methods\nmust be employed to which I have already alluded on the subject of\nmeasurements of length. Professor Michelson, on the one hand, and MM.\nPerot and Fabry, on the other, have devised exceedingly ingenious\nprocesses, which have led to results of really unhoped-for precision.\nThe very exact knowledge also of the speed of the propagation of light\nallows the duration of a vibration to be calculated when once the\nwave-length is known. It is thus found that, in the case of visible\nlight, the number of the vibrations from the end of the violet to the\ninfra-red varies from four hundred to two hundred billions per second.\nThis gamut is not, however, the only one the ether can give. For a\nlong time we have known ultra-violet radiations still more rapid, and,\non the other hand, infra-red ones more slow, while in the last few\nyears the field of known radiations has been singularly extended in\nboth directions.\n\nIt is to M. Rubens and his fellow-workers that are due the most\nbrilliant conquests in the matter of great wave-lengths. He had\nremarked that, in their study, the difficulty of research proceeds\nfrom the fact that the extreme waves of the infra-red spectrum only\ncontain a small part of the total energy emitted by an incandescent\nbody; so that if, for the purpose of study, they are further dispersed\nby a prism or a grating, the intensity at any one point becomes so\nslight as to be no longer observable. His original idea was to obtain,\nwithout prism or grating, a homogeneous pencil of great wave-length\nsufficiently intense to be examined. For this purpose the radiant\nsource used was a strip of platinum covered with fluorine or powdered\nquartz, which emits numerous radiations close to two bands of linear\nabsorption in the absorption spectra of fluorine and quartz, one of\nwhich is situated in the infra-red. The radiations thus emitted are\nseveral times reflected on fluorine or on quartz, as the case may be;\nand as, in proximity to the bands, the absorption is of the order of\nthat of metallic bodies for luminous rays, we no longer meet in the\npencil several times reflected or in the rays _remaining_ after this\nkind of filtration, with any but radiations of great wave-length.\nThus, for instance, in the case of the quartz, in the neighbourhood of\na radiation corresponding to a wave-length of 8.5 microns, the\nabsorption is thirty times greater in the region of the band than in\nthe neighbouring region, and consequently, after three reflexions,\nwhile the corresponding radiations will not have been weakened, the\nneighbouring waves will be so, on the contrary, in the proportion of 1\nto 27,000.\n\nWith mirrors of rock salt and of sylvine[21] there have been obtained,\nby taking an incandescent gas light (Auer) as source, radiations\nextending as far as 70 microns; and these last are the greatest\nwave-lengths observed in optical phenomena. These radiations are\nlargely absorbed by the vapour of water, and it is no doubt owing to\nthis absorption that they are not found in the solar spectrum. On the\nother hand, they easily pass through gutta-percha, india-rubber, and\ninsulating substances in general.\n\n[Footnote 21: A natural chlorate of potassium, generally of volcanic\norigin.--ED.]\n\nAt the opposite end of the spectrum the knowledge of the ultra-violet\nregions has been greatly extended by the researches of Lenard. These\nextremely rapid radiations have been shown by that eminent physicist\nto occur in the light of the electric sparks which flash between two\nmetal points, and which are produced by a large induction coil with\ncondenser and a Wehnelt break. Professor Schumann has succeeded in\nphotographing them by depositing bromide of silver directly on glass\nplates without fixing it with gelatine; and he has, by the same\nprocess, photographed in the spectrum of hydrogen a ray with a\nwave-length of only 0.1 micron.\n\nThe spectroscope was formed entirely of fluor-spar, and a vacuum had\nbeen created in it, for these radiations are extremely absorbable by\nthe air.\n\nNotwithstanding the extreme smallness of the luminous wave-lengths, it\nhas been possible, after numerous fruitless trials, to obtain\nstationary waves analogous to those which, in the case of sound, are\nproduced in organ pipes. The marvellous application M. Lippmann has\nmade of these waves to completely solve the problem of photography in\ncolours is well known. This discovery, so important in itself and so\ninstructive, since it shows us how the most delicate anticipations of\ntheory may be verified in all their consequences, and lead the\nphysicist to the solution of the problems occurring in practice, has\njustly become popular, and there is, therefore, no need to describe it\nhere in detail.\n\nProfessor Wiener obtained stationary waves some little while before M.\nLippmann's discovery, in a layer of a sensitive substance having a\ngrain sufficiently small in relation to the length of wave. His aim\nwas to solve a question of great importance to a complete knowledge of\nthe ether. Fresnel founded his theory of double refraction and\nreflexion by transparent surfaces, on the hypothesis that the\nvibration of a ray of polarized light is perpendicular to the plane of\npolarization. But Neumann has proposed, on the contrary, a theory in\nwhich he recognizes that the luminous vibration is in this very plane.\nHe rather supposes, in opposition to Fresnel's idea, that the density\nof the ether remains the same in all media, while its coefficient of\nelasticity is variable.\n\nVery remarkable experiments on dispersion by M. Carvallo prove indeed\nthat the idea of Fresnel was, if not necessary for us to adopt, at\nleast the more probable of the two; but apart from this indication,\nand contrary to the hypothesis of Neumann, the two theories, from the\npoint of view of the explanation of all known facts, really appear to\nbe equivalent. Are we then in presence of two mechanical explanations,\ndifferent indeed, but nevertheless both adaptable to all the facts,\nand between which it will always be impossible to make a choice? Or,\non the contrary, shall we succeed in realising an _experimentum\ncrucis_, an experiment at the point where the two theories cross,\nwhich will definitely settle the question?\n\nProfessor Wiener thought he could draw from his experiment a firm\nconclusion on the point in dispute. He produced stationary waves with\nlight polarized at an angle of 45 deg.,[22] and established that, when\nlight is polarized in the plane of incidence, the fringes persist; but\nthat, on the other hand, they disappear when the light is polarized\nperpendicularly to this plane. If it be admitted that a photographic\nimpression results from the active force of the vibratory movement of\nthe ether, the question is, in fact, completely elucidated, and the\ndiscrepancy is abolished in Fresnel's favour.\n\n[Footnote 22: That is to say, he reflected the beam of polarized light\nby a mirror placed at that angle. See Turpain, _Lecons elementaires de\nPhysique_, t. ii. p. 311, for details of the experiment.--ED.]\n\nM.H. Poincare has pointed out, however, that we know nothing as to the\nmechanism of the photographic impression. We cannot consider it\nevident that it is the kinetic energy of the ether which produces the\ndecomposition of the sensitive salt; and if, on the contrary, we\nsuppose it to be due to the potential energy, all the conclusions are\nreversed, and Neumann's idea triumphs.\n\nRecently a very clever physicist, M. Cotton, especially known for his\nskilful researches in the domain of optics, has taken up anew the\nstudy of stationary waves. He has made very precise quantitative\nexperiments, and has demonstrated, in his turn, that it is impossible,\neven with spherical waves, to succeed in determining on which of the\ntwo vectors which have to be regarded in all theories of light on the\nsubject of polarization phenomena the luminous intensity and the\nchemical action really depend. This question, therefore, no longer\nexists for those physicists who admit that luminous vibrations are\nelectrical oscillations. Whatever, then, the hypothesis formed,\nwhether it be electric force or, on the contrary, magnetic force which\nwe place in the plane of polarization, the mode of propagation\nforeseen will always be in accord with the facts observed.\n\n\nSec. 3. THE ELECTROMAGNETIC ETHER\n\nThe idea of attributing the phenomena of electricity to perturbations\nproduced in the medium which transmits the light is already of old\nstanding; and the physicists who witnessed the triumph of Fresnel's\ntheories could not fail to conceive that this fluid, which fills the\nwhole of space and penetrates into all bodies, might also play a\npreponderant part in electrical actions. Some even formed too hasty\nhypotheses on this point; for the hour had not arrived when it was\npossible to place them on a sufficiently sound basis, and the known\nfacts were not numerous enough to give the necessary precision.\n\nThe founders of modern electricity also thought it wiser to adopt,\nwith regard to this science, the attitude taken by Newton in\nconnection with gravitation: \"In the first place to observe facts, to\nvary the circumstances of these as much as possible, to accompany this\nfirst work by precise measurements in order to deduce from them\ngeneral laws founded solely on experiment, and to deduce from these\nlaws, independently of all hypotheses on the nature of the forces\nproducing the phenomena, the mathematical value of these forces--that\nis to say, the formula representing them. Such was the system pursued\nby Newton. It has, in general, been adopted in France by the scholars\nto whom physics owe the great progress made of late years, and it has\nserved as my guide in all my researches on electrodynamic\nphenomena.... It is for this reason that I have avoided speaking of\nthe ideas I may have on the nature of the cause of the force emanating\nfrom voltaic conductors.\"\n\nThus did Ampere express himself. The illustrious physicist rightly\nconsidered the results obtained by him through following this wise\nmethod as worthy of comparison with the laws of attraction; but he\nknew that when this first halting-place was reached there was still\nfurther to go, and that the evolution of ideas must necessarily\ncontinue.\n\n\"With whatever physical cause,\" he adds, \"we may wish to connect the\nphenomena produced by electro-dynamic action, the formula I have\nobtained will always remain the expression of the facts,\" and he\nexplicitly indicated that if one could succeed in deducing his formula\nfrom the consideration of the vibrations of a fluid distributed\nthrough space, an enormous step would have been taken in this\ndepartment of physics. He added, however, that this research appeared\nto him premature, and would change nothing in the results of his work,\nsince, to accord with facts, the hypothesis adopted would always have\nto agree with the formula which exactly represents them.\n\nIt is not devoid of interest to observe that Ampere himself,\nnotwithstanding his caution, really formed some hypotheses, and\nrecognized that electrical phenomena were governed by the laws of\nmechanics. Yet the principles of Newton then appeared to be\nunshakable.\n\nFaraday was the first to demonstrate, by clear experiment, the\ninfluence of the media in electricity and magnetic phenomena, and he\nattributed this influence to certain modifications in the ether which\nthese media enclose. His fundamental conception was to reject action\nat a distance, and to localize in the ether the energy whose evolution\nis the cause of the actions manifested, as, for example, in the\ndischarge of a condenser.\n\nConsider the barrel of a pump placed in a vacuum and closed by a\npiston at each end, and let us introduce between these a certain mass\nof air. The two pistons, through the elastic force of the gas, repel\neach other with a force which, according to the law of Mariotte,\nvaries in inverse ratio to the distance. The method favoured by Ampere\nwould first of all allow this law of repulsion between the two pistons\nto be discovered, even if the existence of a gas enclosed in the\nbarrel of the pump were unsuspected; and it would then be natural to\nlocalize the potential energy of the system on the surface of the two\npistons. But if the phenomenon is more carefully examined, we shall\ndiscover the presence of the air, and we shall understand that every\npart of the volume of this air could, if it were drawn off into a\nrecipient of equal volume, carry away with it a fraction of the energy\nof the system, and that consequently this energy belongs really to the\nair and not to the pistons, which are there solely for the purpose of\nenabling this energy to manifest its existence.\n\nFaraday made, in some sort, an equivalent discovery when he perceived\nthat the electrical energy belongs, not to the coatings of the\ncondenser, but to the dielectric which separates them. His audacious\nviews revealed to him a new world, but to explore this world a surer\nand more patient method was needed.\n\nMaxwell succeeded in stating with precision certain points of\nFaraday's ideas, and he gave them the mathematical form which, often\nwrongly, impresses physicists, but which when it exactly encloses a\ntheory, is a certain proof that this theory is at least coherent and\nlogical.[23]\n\n[Footnote 23: It will no doubt be a shock to those whom Professor\nHenry Armstrong has lately called the \"mathematically-minded\" to find\na member of the Poincare family speaking disrespectfully of the\nscience they have done so much to illustrate. One may perhaps compare\nthe expression in the text with M. Henri Poincare's remark in his last\nallocution to the Academie des Sciences, that \"Mathematics are\nsometimes a nuisance, and even a danger, when they induce us to affirm\nmore than we know\" (_Comptes-rendus_, 17th December 1906).]\n\nThe work of Maxwell is over-elaborated, complex, difficult to read,\nand often ill-understood, even at the present day. Maxwell is more\nconcerned in discovering whether it is possible to give an explanation\nof electrical and magnetic phenomena which shall be founded on the\nmechanical properties of a single medium, than in stating this\nexplanation in precise terms. He is aware that if we could succeed in\nconstructing such an interpretation, it would be easy to propose an\ninfinity of others, entirely equivalent from the point of view of the\nexperimentally verifiable consequences; and his especial ambition is\ntherefore to extract from the premises a general view, and to place in\nevidence something which would remain the common property of all the\ntheories.\n\nHe succeeded in showing that if the electrostatic energy of an\nelectromagnetic field be considered to represent potential energy, and\nits electrodynamic the kinetic energy, it becomes possible to satisfy\nboth the principle of least action and that of the conservation of\nenergy; from that moment--if we eliminate a few difficulties which\nexist regarding the stability of the solutions--the possibility of\nfinding mechanical explanations of electromagnetic phenomena must be\nconsidered as demonstrated. He thus succeeded, moreover, in stating\nprecisely the notion of two electric and magnetic fields which\nare produced in all points of space, and which are strictly\ninter-connected, since the variation of the one immediately and\ncompulsorily gives birth to the other.\n\nFrom this hypothesis he deduced that, in the medium where this energy\nis localized, an electromagnetic wave is propagated with a velocity\nequal to the relation of the units of electric mass in the\nelectromagnetic and electrostatic systems. Now, experiments made known\nsince his time have proved that this relation is numerically equal to\nthe speed of light, and the more precise experiments made in\nconsequence--among which should be cited the particularly careful ones\nof M. Max Abraham--have only rendered the coincidence still more\ncomplete.\n\nIt is natural henceforth to suppose that this medium is identical with\nthe luminous ether, and that a luminous wave is an electromagnetic\nwave--that is to say, a succession of alternating currents, which\nexist in the dielectric and even in the void, and possess an enormous\nfrequency, inasmuch as they change their direction thousands of\nbillions of times per second, and by reason of this frequency produce\nconsiderable induction effects. Maxwell did not admit the existence of\nopen currents. To his mind, therefore, an electrical vibration could\nnot produce condensations of electricity. It was, in consequence,\nnecessarily transverse, and thus coincided with the vibration of\nFresnel; while the corresponding magnetic vibration was perpendicular\nto it, and would coincide with the luminous vibration of Neumann.\n\nMaxwell's theory thus establishes a close correlation between the\nphenomena of the luminous and those of the electromagnetic waves, or,\nwe might even say, the complete identity of the two. But it does not\nfollow from this that we ought to regard the variation of an electric\nfield produced at some one point as necessarily consisting of a real\ndisplacement of the ether round that point. The idea of thus bringing\nelectrical phenomena back to the mechanics of the ether is not, then,\nforced upon us, and the contrary idea even seems more probable. It is\nnot the optics of Fresnel which absorbs the science of electricity, it\nis rather the optics which is swallowed up by a more general theory.\nThe attempts of popularizers who endeavour to represent, in all their\ndetails, the mechanism of the electric phenomena, thus appear vain\nenough, and even puerile. It is useless to find out to what material\nbody the ether may be compared, if we content ourselves with seeing in\nit a medium of which, at every point, two vectors define the\nproperties.\n\nFor a long time, therefore, we could remark that the theory of Fresnel\nsimply supposed a medium in which something periodical was propagated,\nwithout its being necessary to admit this something to be a movement;\nbut we had to wait not only for Maxwell, but also for Hertz, before\nthis idea assumed a really scientific shape. Hertz insisted on the\nfact that the six equations of the electric field permit all the\nphenomena to be anticipated without its being necessary to construct\none hypothesis or another, and he put these equations into a very\nsymmetrical form, which brings completely in evidence the perfect\nreciprocity between electrical and magnetic actions. He did yet more,\nfor he brought to the ideas of Maxwell the most striking confirmation\nby his memorable researches on electric oscillations.\n\n\nSec. 4. ELECTRICAL OSCILLATIONS\n\nThe experiments of Hertz are well known. We know how the Bonn\nphysicist developed, by means of oscillating electric discharges,\ndisplacement currents and induction effects in the whole of the space\nround the spark-gap; and how he excited by induction at some point in\na wire a perturbation which afterwards is propagated along the wire,\nand how a resonator enabled him to detect the effect produced.\n\nThe most important point made evident by the observation of\ninterference phenomena and subsequently verified directly by M.\nBlondlot, is that the electromagnetic perturbation is propagated with\nthe speed of light, and this result condemns for ever all the\nhypotheses which fail to attribute any part to the intervening media\nin the propagation of an induction phenomenon.\n\nIf the inducing action were, in fact, to operate directly between the\ninducing and the induced circuits, the propagation should be\ninstantaneous; for if an interval were to occur between the moment\nwhen the cause acted and the one when the effect was produced, during\nthis interval there would no longer be anything anywhere, since the\nintervening medium does not come into play, and the phenomenon would\nthen disappear.\n\nLeaving on one side the manifold but purely electrical consequences of\nthis and the numerous researches relating to the production or to the\nproperties of the waves--some of which, those of MM. Sarrazin and de\nla Rive, Righi, Turpain, Lebedeff, Decombe, Barbillon, Drude, Gutton,\nLamotte, Lecher, etc., are, however, of the highest order--I shall\nonly mention here the studies more particularly directed to the\nestablishment of the identity of the electromagnetic and the luminous\nwaves.\n\nThe only differences which subsist are necessarily those due to the\nconsiderable discrepancy which exists between the durations of the\nperiods of these two categories of waves. The length of wave\ncorresponding to the first spark-gap of Hertz was about 6 metres, and\nthe longest waves perceptible by the retina are 7/10 of a micron.[24]\n\n[Footnote 24: See footnote 3.]\n\nThese radiations are so far apart that it is not astonishing that\ntheir properties have not a perfect similitude. Thus phenomena like\nthose of diffraction, which are negligible in the ordinary conditions\nunder which light is observed, may here assume a preponderating\nimportance. To play the part, for example, with the Hertzian waves,\nwhich a mirror 1 millimetre square plays with regard to light, would\nrequire a colossal mirror which would attain the size of a\nmyriametre[25] square.\n\n[Footnote 25: I.e., 10,000 metres.--ED.]\n\nThe efforts of physicists have to-day, however, filled up, in great\npart, this interval, and from both banks at once they have laboured to\nbuild a bridge between the two domains. We have seen how Rubens showed\nus calorific rays 60 metres long; on the other hand, MM. Lecher, Bose,\nand Lampa have succeeded, one after the other, in gradually obtaining\noscillations with shorter and shorter periods. There have been\nproduced, and are now being studied, electromagnetic waves of four\nmillimetres; and the gap subsisting in the spectrum between the rays\nleft undetected by sylvine and the radiations of M. Lampa now hardly\ncomprise more than five octaves--that is to say, an interval\nperceptibly equal to that which separates the rays observed by M.\nRubens from the last which are evident to the eye.\n\nThe analogy then becomes quite close, and in the remaining rays the\nproperties, so to speak, characteristic of the Hertzian waves, begin\nto appear. For these waves, as we have seen, the most transparent\nbodies are the most perfect electrical insulators; while bodies still\nslightly conducting are entirely opaque. The index of refraction of\nthese substances tends in the case of great wave-lengths to become, as\nthe theory anticipates, nearly the square root of the dielectric\nconstant.\n\nMM. Rubens and Nichols have even produced with the waves which remain\nphenomena of electric resonance quite similar to those which an\nItalian scholar, M. Garbasso, obtained with electric waves. This\nphysicist showed that, if the electric waves are made to impinge on a\nflat wooden stand, on which are a series of resonators parallel to\neach other and uniformly arranged, these waves are hardly reflected\nsave in the case where the resonators have the same period as the\nspark-gap. If the remaining rays are allowed to fall on a glass plate\nsilvered and divided by a diamond fixed on a dividing machine into\nsmall rectangles of equal dimensions, there will be observed\nvariations in the reflecting power according to the orientation of the\nrectangles, under conditions entirely comparable with the experiment\nof Garbasso.\n\nIn order that the phenomenon be produced it is necessary that the\nremaining waves should be previously polarized. This is because, in\nfact, the mechanism employed to produce the electric oscillations\nevidently gives out vibrations which occur on a single plane and are\nsubsequently polarized.\n\nWe cannot therefore entirely assimilate a radiation proceeding from a\nspark-gap to a ray of natural light. For the synthesis of light to be\nrealized, still other conditions must be complied with. During a\nluminous impression, the direction and the phase change millions of\ntimes in the vibration sensible to the retina, yet the damping of this\nvibration is very slow. With the Hertzian oscillations all these\nconditions are changed--the damping is very rapid but the direction\nremains invariable.\n\nEvery time, however, that we deal with general phenomena which are\nindependent of these special conditions, the parallelism is perfect;\nand with the waves, we have put in evidence the reflexion, refraction,\ntotal reflexion, double reflexion, rotatory polarization, dispersion,\nand the ordinary interferences produced by rays travelling in the same\ndirection and crossing each other at a very acute angle, or the\ninterferences analogous to those which Wiener observed with rays of\nthe contrary direction.\n\nA very important consequence of the electromagnetic theory foreseen by\nMaxwell is that the luminous waves which fall on a surface must\nexercise on this surface a pressure equal to the radiant energy which\nexists in the unit of volume of the surrounding space. M. Lebedeff a\nfew years ago allowed a sheaf of rays from an arc lamp to fall on a\ndeflection radiometer,[26] and thus succeeded in revealing the\nexistence of this pressure. Its value is sufficient, in the case of\nmatter of little density and finely divided, to reduce and even change\ninto repulsion the attractive action exercised on bodies by the sun.\nThis is a fact formerly conjectured by Faye, and must certainly play a\ngreat part in the deformation of the heads of comets.\n\n[Footnote 26: By this M. Poincare appears to mean a radiometer in\nwhich the vanes are not entirely free to move as in the radiometer of\nCrookes but are suspended by one or two threads as in the instrument\ndevised by Professor Poynting.--ED.]\n\nMore recently, MM. Nichols and Hull have undertaken experiments on\nthis point. They have measured not only the pressure, but also the\nenergy of the radiation by means of a special bolometer. They have\nthus arrived at numerical verifications which are entirely in\nconformity with the calculations of Maxwell.\n\nThe existence of these pressures may be otherwise foreseen even apart\nfrom the electromagnetic theory, by adding to the theory of\nundulations the principles of thermodynamics. Bartoli, and more\nrecently Dr Larmor, have shown, in fact, that if these pressures did\nnot exist, it would be possible, without any other phenomenon, to pass\nheat from a cold into a warm body, and thus transgress the principle\nof Carnot.\n\n\nSec. 5. THE X RAYS\n\nIt appears to-day quite probable that the X rays should be classed\namong the phenomena which have their seat in the luminous ether.\nDoubtless it is not necessary to recall here how, in December 1895,\nRoentgen, having wrapped in black paper a Crookes tube in action,\nobserved that a fluorescent platinocyanide of barium screen placed in\nthe neighbourhood, had become visible in the dark, and that a\nphotographic plate had received an impress. The rays which come from\nthe tube, in conditions now well known, are not deviated by a magnet,\nand, as M. Curie and M. Sagnac have conclusively shown, they carry no\nelectric charge. They are subject to neither reflection nor\nrefraction, and very precise and very ingenious measurements by M.\nGouy have shown that, in their case, the refraction index of the\nvarious bodies cannot be more than a millionth removed from unity.\n\nWe knew from the outset that there existed various X rays differing\nfrom each other as, for instance, the colours of the spectrum, and\nthese are distinguished from each other by their unequal power of\npassing through substances. M. Sagnac, particularly, has shown that\nthere can be obtained a gradually decreasing scale of more or less\nabsorbable rays, so that the greater part of their photographic action\nis stopped by a simple sheet of black paper. These rays figure among\nthe secondary rays discovered, as is known, by this ingenious\nphysicist. The X rays falling on matter are thus subjected to\ntransformations which may be compared to those which the phenomena of\nluminescence produce on the ultra-violet rays.\n\nM. Benoist has founded on the transparency of matter to the rays a\nsure and practical method of allowing them to be distinguished, and\nhas thus been enabled to define a specific character analogous to the\ncolour of the rays of light. It is probable also that the different\nrays do not transport individually the same quantity of energy. We\nhave not yet obtained on this point precise results, but it is roughly\nknown, since the experiments of MM. Rutherford and M'Clung, what\nquantity of energy corresponds to a pencil of X rays. These physicists\nhave found that this quantity would be, on an average, five hundred\ntimes larger than that brought by an analogous pencil of solar light\nto the surface of the earth. What is the nature of this energy? The\nquestion does not appear to have been yet solved.\n\nIt certainly appears, according to Professors Haga and Wind and to\nProfessor Sommerfeld, that with the X rays curious experiments of\ndiffraction may be produced. Dr Barkla has shown also that they can\nmanifest true polarization. The secondary rays emitted by a metallic\nsurface when struck by X rays vary, in fact, in intensity when the\nposition of the plane of incidence round the primary pencil is\nchanged. Various physicists have endeavoured to measure the speed of\npropagation, but it seems more and more probable that it is very\nnearly that of light.[27]\n\n[Footnote 27: See especially the experiments of Professor E. Marx\n(Vienna), _Annalen der Physik_, vol. xx. (No. 9 of 1906), pp. 677 _et\nseq._, which seem conclusive on this point.--ED.]\n\nI must here leave out the description of a crowd of other experiments.\nSome very interesting researches by M. Brunhes, M. Broca, M.\nColardeau, M. Villard, in France, and by many others abroad, have\npermitted the elucidation of several interesting problems relative to\nthe duration of the emission or to the best disposition to be adopted\nfor the production of the rays. The only point which will detain us is\nthe important question as to the nature of the X rays themselves; the\nproperties which have just been brought to mind are those which appear\nessential and which every theory must reckon with.\n\nThe most natural hypothesis would be to consider the rays as\nultra-violet radiations of very short wave-length, or radiations which\nare in a manner ultra-ultra-violet. This interpretation can still, at\nthis present moment, be maintained, and the researches of MM. Buisson,\nRighi, Lenard, and Merrit Stewart have even established that rays of\nvery short wave-lengths produce on metallic conductors, from the point\nof view of electrical phenomena, effects quite analogous to those of\nthe X rays. Another resemblance results also from the experiments by\nwhich M. Perreau established that these rays act on the electric\nresistance of selenium. New and valuable arguments have thus added\nforce to those who incline towards a theory which has the merit of\nbringing a new phenomenon within the pale of phenomena previously\nknown.\n\nNevertheless the shortest ultra-violet radiations, such as those of M.\nSchumann, are still capable of refraction by quartz, and this\ndifference constitutes, in the minds of many physicists, a serious\nenough reason to decide them to reject the more simple hypothesis.\nMoreover, the rays of Schumann are, as we have seen, extraordinarily\nabsorbable,--so much so that they have to be observed in a vacuum. The\nmost striking property of the X rays is, on the contrary, the facility\nwith which they pass through obstacles, and it is impossible not to\nattach considerable importance to such a difference.\n\nSome attribute this marvellous radiation to longitudinal vibrations,\nwhich, as M. Duhem has shown, would be propagated in dielectric media\nwith a speed equal to that of light. But the most generally accepted\nidea is the one formulated from the first by Sir George Stokes and\nfollowed up by Professor Wiechert. According to this theory the X rays\nshould be due to a succession of independent pulsations of the ether,\nstarting from the points where the molecules projected by the cathode\nof the Crookes tube meet the anticathode. These pulsations are not\ncontinuous vibrations like the radiations of the spectrum; they are\nisolated and extremely short; they are, besides, transverse, like the\nundulations of light, and the theory shows that they must be\npropagated with the speed of light. They should present neither\nrefraction nor reflection, but, under certain conditions, they may be\nsubject to the phenomena of diffraction. All these characteristics are\nfound in the Roentgen rays.\n\nProfessor J.J. Thomson adopts an analogous idea, and states the\nprecise way in which the pulsations may be produced at the moment when\nthe electrified particles forming the cathode rays suddenly strike the\nanticathode wall. The electromagnetic induction behaves in such a way\nthat the magnetic field is not annihilated when the particle stops,\nand the new field produced, which is no longer in equilibrium, is\npropagated in the dielectric like an electric pulsation. The electric\nand magnetic pulsations excited by this mechanism may give birth to\neffects similar to those of light. Their slight amplitude, however, is\nthe cause of there here being neither refraction nor diffraction\nphenomena, save in very special conditions. If the cathode particle is\nnot stopped in zero time, the pulsation will take a greater amplitude,\nand be, in consequence, more easily absorbable; to this is probably to\nbe attributed the differences which may exist between different tubes\nand different rays.\n\nIt is right to add that some authors, notwithstanding the proved\nimpossibility of deviating them in a magnetic field, have not\nrenounced the idea of comparing them with the cathode rays. They\nsuppose, for instance, that the rays are formed by electrons animated\nwith so great a velocity that their inertia, conformably with theories\nwhich I shall examine later, no longer permit them to be stopped in\ntheir course; this is, for instance, the theory upheld by Mr\nSutherland. We know, too, that to M. Gustave Le Bon they represent the\nextreme limit of material things, one of the last stages before the\nvanishing of matter on its return to the ether.\n\nEveryone has heard of the N rays, whose name recalls the town of\nNancy, where they were discovered. In some of their singular\nproperties they are akin to the X rays, while in others they are\nwidely divergent from them.\n\nM. Blondlot, one of the masters of contemporary physics, deeply\nrespected by all who know him, admired by everyone for the penetration\nof his mind, and the author of works remarkable for the originality\nand sureness of his method, discovered them in radiations emitted from\nvarious sources, such as the sun, an incandescent light, a Nernst\nlamp, and even bodies previously exposed to the sun's rays. The\nessential property which allows them to be revealed is their action on\na small induction spark, of which they increase the brilliancy; this\nphenomenon is visible to the eye and is rendered objective by\nphotography.\n\nVarious other physicists and numbers of physiologists, following the\npath opened by M. Blondlot, published during 1903 and 1904 manifold\nbut often rather hasty memoirs, in which they related the results of\ntheir researches, which do not appear to have been always conducted\nwith the accuracy desirable. These results were most strange; they\nseemed destined to revolutionise whole regions not only of the domain\nof physics, but likewise of the biological sciences. Unfortunately the\nmethod of observation was always founded on the variations in\nvisibility of the spark or of a phosphorescent substance, and it soon\nbecame manifest that these variations were not perceptible to all\neyes.\n\nNo foreign experimenter has succeeded in repeating the experiments,\nwhile in France many physicists have failed; and hence the question\nhas much agitated public opinion. Are we face to face with a very\nsingular case of suggestion, or is special training and particular\ndispositions required to make the phenomenon apparent? It is not\npossible, at the present moment, to declare the problem solved; but\nvery recent experiments by M. Gutton and a note by M. Mascart have\nreanimated the confidence of those who hoped that such a scholar as M.\nBlondlot could not have been deluded by appearances. However, these\nlast proofs in favour of the existence of the rays have themselves\nbeen contested, and have not succeeded in bringing conviction to\neveryone.\n\nIt seems very probable indeed that certain of the most singular\nconclusions arrived at by certain authors on the subject will lapse\ninto deserved oblivion. But negative experiments prove nothing in a\ncase like this, and the fact that most experimenters have failed where\nM. Blondlot and his pupils have succeeded may constitute a\npresumption, but cannot be regarded as a demonstrative argument. Hence\nwe must still wait; it is exceedingly possible that the illustrious\nphysicist of Nancy may succeed in discovering objective actions of the\nN rays which shall be indisputable, and may thus establish on a firm\nbasis a discovery worthy of those others which have made his name so\njustly celebrated.\n\nAccording to M. Blondlot the N rays can be polarised, refracted, and\ndispersed, while they have wavelengths comprised within .0030 micron,\nand .0760 micron--that is to say, between an eighth and a fifth of\nthat found for the extreme ultra-violet rays. They might be, perhaps,\nsimply rays of a very short period. Their existence, stripped of the\nparasitical and somewhat singular properties sought to be attributed\nto them, would thus appear natural enough. It would, moreover, be\nextremely important, and lead, no doubt, to most curious applications;\nit can be conceived, in fact, that such rays might serve to reveal\nwhat occurs in those portions of matter whose too minute dimensions\nescape microscopic examination on account of the phenomena of\ndiffraction.\n\nFrom whatever point of view we look at it, and whatever may be the\nfate of the discovery, the history of the N rays is particularly\ninstructive, and must give food for reflection to those interested in\nquestions of scientific methods.\n\n\nSec. 6. THE ETHER AND GRAVITATION\n\nThe striking success of the hypothesis of the ether in optics has, in\nour own days, strengthened the hope of being able to explain, by an\nanalogous representation, the action of gravitation.\n\nFor a long time, philosophers who rejected the idea that ponderability\nis a primary and essential quality of all bodies have sought to reduce\ntheir weight to pressures exercised in a very subtle fluid. This was\nthe conception of Descartes, and was perhaps the true idea of Newton\nhimself. Newton points out, in many passages, that the laws he had\ndiscovered were independent of the hypotheses that could be formed on\nthe way in which universal attraction was produced, but that with\nsufficient experiments the true cause of this attraction might one day\nbe reached. In the preface to the second edition of the Optics he\nwrites: \"To prove that I have not considered weight as a universal\nproperty of bodies, I have added a question as to its cause,\npreferring this form of question because my interpretation does not\nentirely satisfy me in the absence of experiment\"; and he puts the\nquestion in this shape: \"Is not this medium (the ether) more rarefied\nin the interior of dense bodies like the sun, the planets, the comets,\nthan in the empty spaces which separate them? Passing from these\nbodies to great distances, does it not become continually denser, and\nin that way does it not produce the weight of these great bodies with\nregard to each other and of their parts with regard to these bodies,\neach body tending to leave the most dense for the most rarefied\nparts?\"\n\nEvidently this view is incomplete, but we may endeavour to state it\nprecisely. If we admit that this medium, the properties of which would\nexplain the attraction, is the same as the luminous ether, we may\nfirst ask ourselves whether the action of gravitation is itself also\ndue to oscillations. Some authors have endeavoured to found a theory\non this hypothesis, but we are immediately brought face to face with\nvery serious difficulties. Gravity appears, in fact, to present quite\nexceptional characteristics. No agent, not even those which depend\nupon the ether, such as light and electricity, has any influence on\nits action or its direction. All bodies are, so to speak, absolutely\ntransparent to universal attraction, and no experiment has succeeded\nin demonstrating that its propagation is not instantaneous. From\nvarious astronomical observations, Laplace concluded that its\nvelocity, in any case, must exceed fifty million times that of light.\nIt is subject neither to reflection nor to refraction; it is\nindependent of the structure of bodies; and not only is it\ninexhaustible, but also (as is pointed out, according to M. Hannequin,\nby an English scholar, James Croll) the distribution of the effects of\nthe attracting force of a mass over the manifold particles which may\nsuccessively enter the field of its action in no way diminishes the\nattraction it exercises on each of them respectively, a thing which is\nseen nowhere else in nature.\n\nNevertheless it is possible, by means of certain hypotheses, to\nconstruct interpretations whereby the appropriate movements of an\nelastic medium should explain the facts clearly enough. But these\nmovements are very complex, and it seems almost inconceivable that the\nsame medium could possess simultaneously the state of movement\ncorresponding to the transmission of a luminous phenomenon and that\nconstantly imposed on it by the transmission of gravitation.\n\nAnother celebrated hypothesis was devised by Lesage, of Geneva. Lesage\nsupposed space to be overrun in all directions by currents of\n_ultramundane_ corpuscles. This hypothesis, contested by Maxwell, is\ninteresting. It might perhaps be taken up again in our days, and it is\nnot impossible that the assimilation of these corpuscles to electrons\nmight give a satisfactory image.[28]\n\n[Footnote 28: M. Sagnac (_Le Radium_, Jan. 1906, p. 14), following\nperhaps Professors Elster and Geitel, has lately taken up this idea\nanew.--ED.]\n\nM. Cremieux has recently undertaken experiments directed, as he\nthinks, to showing that the divergences between the phenomena of\ngravitation and all the other phenomena in nature are more apparent\nthan real. Thus the evolution in the heart of the ether of a quantity\nof gravific energy would not be entirely isolated, and as in the case\nof all evolutions of all energy of whatever kind, it should provoke a\npartial transformation into energy of a different form. Thus again the\nliberated energy of gravitation would vary when passing from one\nmaterial to another, as from gases into liquids, or from one liquid to\na different one.\n\nOn this last point the researches of M. Cremieux have given\naffirmative results: if we immerse in a large mass of some liquid\nseveral drops of another not miscible with the first, but of identical\ndensity, we form a mass representing no doubt a discontinuity in the\nether, and we may ask ourselves whether, in conformity with what\nhappens in all other phenomena of nature, this discontinuity has not a\ntendency to disappear.\n\nIf we abide by the ordinary consequences of the Newtonian theory of\npotential, the drops should remain motionless, the hydrostatic\nimpulsion forming an exact equilibrium to their mutual attraction. Now\nM. Cremieux remarks that, as a matter of fact, they slowly approach\neach other.\n\nSuch experiments are very delicate; and with all the precautions taken\nby the author, it cannot yet be asserted that he has removed all\npossibility of the action of the phenomena of capillarity nor all\npossible errors proceeding from extremely slight differences of\ntemperature. But the attempt is interesting and deserves to be\nfollowed up.\n\nThus, the hypothesis of the ether does not yet explain all the\nphenomena which the considerations relating to matter are of\nthemselves powerless to interpret. If we wished to represent to\nourselves, by the mechanical properties of a medium filling the whole\nof the universe, all luminous, electric, and gravitation phenomena, we\nshould be led to attribute to this medium very strange and almost\ncontradictory characteristics; and yet it would be still more\ninconceivable that this medium should be double or treble, that there\nshould be two or three ethers each occupying space as if it were\nalone, and interpenetrating it without exercising any action on one\nanother. We are thus brought, by a close examination of facts, rather\nto the idea that the properties of the ether are not wholly reducible\nto the rules of ordinary mechanics.\n\nThe physicist has therefore not yet succeeded in answering the\nquestion often put to him by the philosopher: \"Has the ether really an\nobjective existence?\" However, it is not necessary to know the answer\nin order to utilize the ether. In its ideal properties we find the\nmeans of determining the form of equations which are valid, and to the\nlearned detached from all metaphysical prepossession this is the\nessential point.\n\n\n\n\nCHAPTER VII\n\nA CHAPTER IN THE HISTORY OF SCIENCE: WIRELESS TELEGRAPHY\n\n\nSec. 1\n\nI have endeavoured in this book to set forth impartially the ideas\ndominant at this moment in the domain of physics, and to make known\nthe facts essential to them. I have had to quote the authors of the\nprincipal discoveries in order to be able to class and, in some sort,\nto name these discoveries; but I in no way claim to write even a\nsummary history of the physics of the day.\n\nI am not unaware that, as has often been said, contemporary history is\nthe most difficult of all histories to write. A certain step backwards\nseems necessary in order to enable us to appreciate correctly the\nrelative importance of events, and details conceal the full view from\neyes which are too close to them, as the trees prevent us from seeing\nthe forest. The event which produces a great sensation has often only\ninsignificant consequences; while another, which seemed at the outset\nof the least importance and little worthy of note, has in the long run\na widespread and deep influence.\n\nIf, however, we deal with the history of a positive discovery,\ncontemporaries who possess immediate information, and are in a\nposition to collect authentic evidence at first hand, will make, by\nbringing to it their sincere testimony, a work of erudition which may\nbe very useful, but which we may be tempted to look upon as very easy\nof execution. Yet such a labour, even when limited to the study of a\nvery minute question or of a recent invention, is far from being\naccomplished without the historian stumbling over serious obstacles.\n\nAn invention is never, in reality, to be attributed to a single\nauthor. It is the result of the work of many collaborators who\nsometimes have no acquaintance with one another, and is often the\nfruit of obscure labours. Public opinion, however, wilfully simple in\nface of a sensational discovery, insists that the historian should\nalso act as judge; and it is the historian's task to disentangle the\ntruth in the midst of the contest, and to declare infallibly to whom\nthe acknowledgments of mankind should be paid. He must, in his\ncapacity as skilled expert, expose piracies, detect the most carefully\nhidden plagiarisms, and discuss the delicate question of priority;\nwhile he must not be deluded by those who do not fear to announce, in\nbold accents, that they have solved problems of which they find the\nsolution imminent, and who, the day after its final elucidation by\nthird parties, proclaim themselves its true discoverers. He must rise\nabove a partiality which deems itself excusable because it proceeds\nfrom national pride; and, finally, he must seek with patience for what\nhas gone before. While thus retreating step by step he runs the risk\nof losing himself in the night of time.\n\nAn example of yesterday seems to show the difficulties of such a task.\nAmong recent discoveries the invention of wireless telegraphy is one\nof those which have rapidly become popular, and looks, as it were, an\nexact subject clearly marked out. Many attempts have already been made\nto write its history. Mr J.J. Fahie published in England as early as\n1899 an interesting work entitled the _History of Wireless\nTelegraphy_; and about the same time M. Broca published in France a\nvery exhaustive work named _La Telegraphie sans fil_. Among the\nreports presented to the Congres international de physique (Paris,\n1900), Signor Righi, an illustrious Italian scholar, whose personal\nefforts have largely contributed to the invention of the present\nsystem of telegraphy, devoted a chapter, short, but sufficiently\ncomplete, of his masterly report on Hertzian waves, to the history of\nwireless telegraphy. The same author, in association with Herr\nBernhard Dessau, has likewise written a more important work, _Die\nTelegraphie ohne Draht_; and _La Telegraphie sans fil et les ondes\nElectriques_ of MM. J. Boulanger and G. Ferrie may also be consulted\nwith advantage, as may _La Telegraphie sans fil_ of Signor Dominico\nMazotto. Quite recently Mr A. Story has given us in a little volume\ncalled _The Story of Wireless Telegraphy_, a condensed but very\nprecise recapitulation of all the attempts which have been made to\nestablish telegraphic communication without the intermediary of a\nconducting wire. Mr Story has examined many documents, has sometimes\nbrought curious facts to light, and has studied even the most recently\nadopted apparatus.\n\nIt may be interesting, by utilising the information supplied by these\nauthors and supplementing them when necessary by others, to trace the\nsources of this modern discovery, to follow its developments, and thus\nto prove once more how much a matter, most simple in appearance,\ndemands extensive and complex researches on the part of an author\ndesirous of writing a definitive work.\n\n\nSec. 2\n\nThe first, and not the least difficulty, is to clearly define the\nsubject. The words \"wireless telegraphy,\" which at first seem to\ncorrespond to a simple and perfectly clear idea, may in reality apply\nto two series of questions, very different in the mind of a physicist,\nbetween which it is important to distinguish. The transmission of\nsignals demands three organs which all appear indispensable: the\ntransmitter, the receiver, and, between the two, an intermediary\nestablishing the communication. This intermediary is generally the\nmost costly part of the installation and the most difficult to set up,\nwhile it is here that the sensible losses of energy at the expense of\ngood output occur. And yet our present ideas cause us to consider this\nintermediary as more than ever impossible to suppress; since, if we\nare definitely quit of the conception of action at a distance, it\nbecomes inconceivable to us that energy can be communicated from one\npoint to another without being carried by some intervening medium.\nBut, practically, the line will be suppressed if, instead of\nconstructing it artificially, we use to replace it one of the natural\nmedia which separate two points on the earth. These natural media are\ndivided into two very distinct categories, and from this\nclassification arise two series of questions to be examined.\n\nBetween the two points in question there are, first, the material\nmedia such as the air, the earth, and the water. For a long time we\nhave used for transmissions to a distance the elastic properties of\nthe air, and more recently the electric conductivity of the soil and\nof water, particularly that of the sea.\n\nModern physics leads us on the other hand, as we have seen, to\nconsider that there exists throughout the whole of the universe\nanother and more subtle medium which penetrates everywhere, is endowed\nwith elasticity _in vacuo_, and retains its elasticity when it\npenetrates into a great number of bodies, such as the air. This medium\nis the luminous ether which possesses, as we cannot doubt, the\nproperty of being able to transmit energy, since it itself brings to\nus by far the larger part of the energy which we possess on earth and\nwhich we find in the movements of the atmosphere, or of waterfalls,\nand in the coal mines proceeding from the decomposition of carbon\ncompounds under the influence of the solar energy. For a long time\nalso before the existence of the ether was known, the duty of\ntransmitting signals was entrusted to it. Thus through the ages a\ndouble evolution is unfolded which has to be followed by the historian\nwho is ambitious of completeness.\n\n\nSec. 3\n\nIf such an historian were to examine from the beginning the first\norder of questions, he might, no doubt, speak only briefly of the\nattempts earlier than electric telegraphy. Without seeking to be\nparadoxical, he certainly ought to mention the invention of the\nspeaking-trumpet and other similar inventions which for a long time\nhave enabled mankind, by the ingenious use of the elastic properties\nof the natural media, to communicate at greater distances than they\ncould have attained without the aid of art. After this in some sort\nprehistoric period had been rapidly run through, he would have to\nfollow very closely the development of electric telegraphy. Almost\nfrom the outset, and shortly after Ampere had made public the idea of\nconstructing a telegraph, and the day after Gauss and Weber set up\nbetween their houses in Goettingen the first line really used, it was\nthought that the conducting properties of the earth and water might be\nmade of service.\n\nThe history of these trials is very long, and is closely mixed up with\nthe history of ordinary telegraphy; long chapters for some time past\nhave been devoted to it in telegraphic treatises. It was in 1838,\nhowever, that Professor C.A. Steinheil of Munich expressed, for the\nfirst time, the clear idea of suppressing the return wire and\nreplacing it by a connection of the line wire to the earth. He thus at\none step covered half the way, the easiest, it is true, which was to\nlead to the final goal, since he saved the use of one-half of the line\nof wire. Steinheil, advised, perhaps, by Gauss, had, moreover, a very\nexact conception of the part taken by the earth considered as a\nconducting body. He seems to have well understood that, in certain\nconditions, the resistance of such a conductor, though supposed to be\nunlimited, might be independent of the distance apart of the\nelectrodes which carry the current and allow it to go forth. He\nlikewise thought of using the railway lines to transmit telegraphic\nsignals.\n\nSeveral scholars who from the first had turned their minds to\ntelegraphy, had analogous ideas. It was thus that S.F.B. Morse,\nsuperintendent of the Government telegraphs in the United States,\nwhose name is universally known in connection with the very simple\napparatus invented by him, made experiments in the autumn of 1842\nbefore a special commission in New York and a numerous public\naudience, to show how surely and how easily his apparatus worked. In\nthe very midst of his experiments a very happy idea occurred to him of\nreplacing by the water of a canal, the length of about a mile of wire\nwhich had been suddenly and accidentally destroyed. This accident,\nwhich for a moment compromised the legitimate success the celebrated\nengineer expected, thus suggested to him a fruitful idea which he did\nnot forget. He subsequently repeated attempts to thus utilise the\nearth and water, and obtained some very remarkable results.\n\nIt is not possible to quote here all the researches undertaken with\nthe same purpose, to which are more particularly attached the names of\nS.W. Wilkins, Wheatstone, and H. Highton, in England; of Bonetti in\nItaly, Gintl in Austria, Bouchot and Donat in France; but there are\nsome which cannot be recalled without emotion.\n\nOn the 17th December 1870, a physicist who has left in the University\nof Paris a lasting name, M. d'Almeida, at that time Professor at the\nLycee Henri IV. and later Inspector-General of Public Instruction,\nquitted Paris, then besieged, in a balloon, and descended in the midst\nof the German lines. He succeeded, after a perilous journey, in\ngaining Havre by way of Bordeaux and Lyons; and after procuring the\nnecessary apparatus in England, he descended the Seine as far as\nPoissy, which he reached on the 14th January 1871. After his\ndeparture, two other scholars, MM. Desains and Bourbouze, relieving\neach other day and night, waited at Paris, in a wherry on the Seine,\nready to receive the signal which they awaited with patriotic anxiety.\nIt was a question of working a process devised by the last-named pair,\nin which the water of the river acted the part of the line wire. On\nthe 23rd January the communication at last seemed to be established,\nbut unfortunately, first the armistice and then the surrender of Paris\nrendered useless the valuable result of this noble effort.\n\nSpecial mention is also due to the experiments made by the Indian\nTelegraph Office, under the direction of Mr Johnson and afterwards of\nMr W.F. Melhuish. They led, indeed, in 1889 to such satisfactory\nresults that a telegraph service, in which the line wire was replaced\nby the earth, worked practically and regularly. Other attempts were\nalso made during the latter half of the nineteenth century to transmit\nsignals through the sea. They preceded the epoch when, thanks to\nnumerous physicists, among whom Lord Kelvin undoubtedly occupies a\npreponderating position, we succeeded in sinking the first cable; but\nthey were not abandoned, even after that date, for they gave hopes of\na much more economical solution of the problem. Among the most\ninteresting are remembered those that S.W. Wilkins carried on for a\nlong time between France and England. Like Cooke and Wheatstone, he\nthought of using as a receiver an apparatus which in some features\nresembles the present receiver of the submarine telegraph. Later,\nGeorge E. Dering, then James Bowman and Lindsay, made on the same\nlines trials which are worthy of being remembered.\n\nBut it is only in our own days that Sir William H. Preece at last\nobtained for the first time really practical results. Sir William\nhimself effected and caused to be executed by his associates--he is\nchief consulting engineer to the General Post Office in England--\nresearches conducted with much method and based on precise theoretical\nconsiderations. He thus succeeded in establishing very easy, clear,\nand regular communications between various places; for example, across\nthe Bristol Channel. The long series of operations accomplished by so\nmany seekers, with the object of substituting a material and natural\nmedium for the artificial lines of metal, thus met with an undoubted\nsuccess which was soon to be eclipsed by the widely-known experiments\ndirected into a different line by Marconi.\n\nIt is right to add that Sir William Preece had himself utilised\ninduction phenomena in his experiments, and had begun researches with\nthe aid of electric waves. Much is due to him for the welcome he gave\nto Marconi; it is certainly thanks to the advice and the material\nsupport he found in Sir William that the young scholar succeeded in\neffecting his sensational experiments.\n\n\nSec. 4\n\nThe starting-point of the experiments based on the properties of the\nluminous ether, and having for their object the transmission of\nsignals, is very remote; and it would be a very laborious task to hunt\nup all the work accomplished in that direction, even if we were to\nconfine ourselves to those in which electrical reactions play a part.\nAn electric reaction, an electrostatic influence, or an\nelectromagnetic phenomenon, is transmitted at a distance through the\nair by the intermediary of the luminous ether. But electric influence\ncan hardly be used, as the distances it would allow us to traverse\nwould be much too restricted, and electrostatic actions are often very\nerratic. The phenomena of induction, which are very regular and\ninsensible to the variations of the atmosphere, have, on the other\nhand, for a long time appeared serviceable for telegraphic purposes.\n\nWe might find, in a certain number of the attempts just mentioned, a\npartial employment of these phenomena. Lindsay, for instance, in his\nproject of communication across the sea, attributed to them a\nconsiderable role. These phenomena even permitted a true telegraphy\nwithout intermediary wire between the transmitter and the receiver, at\nvery restricted distances, it is true, but in peculiarly interesting\nconditions. It is, in fact, owing to them that C. Brown, and later\nEdison and Gilliland, succeeded in establishing communications with\ntrains in motion.\n\nMr Willoughby S. Smith and Mr Charles A. Stevenson also undertook\nexperiments during the last twenty years, in which they used\ninduction, but the most remarkable attempts are perhaps those of\nProfessor Emile Rathenau. With the assistance of Professor Rubens and\nof Herr W. Rathenau, this physicist effected, at the request of the\nGerman Ministry of Marine, a series of researches which enabled him,\nby means of a compound system of conduction and induction by\nalternating currents, to obtain clear and regular communications at a\ndistance of four kilometres. Among the precursors also should be\nmentioned Graham Bell; the inventor of the telephone thought of\nemploying his admirable apparatus as a receiver of induction phenomena\ntransmitted from a distance; Edison, Herr Sacher of Vienna, M. Henry\nDufour of Lausanne, and Professor Trowbridge of Boston, also made\ninteresting attempts in the same direction.\n\nIn all these experiments occurs the idea of employing an oscillating\ncurrent. Moreover, it was known for a long time--since, in 1842, the\ngreat American physicist Henry proved that the discharges from a\nLeyden jar in the attic of his house caused sparks in a metallic\ncircuit on the ground floor--that a flux which varies rapidly and\nperiodically is much more efficacious than a simple flux, which latter\ncan only produce at a distance a phenomenon of slight intensity. This\nidea of the oscillating current was closely akin to that which was at\nlast to lead to an entirely satisfactory solution: that is, to a\nsolution which is founded on the properties of electric waves.\n\n\nSec. 5\n\nHaving thus got to the threshold of the definitive edifice, the\nhistorian, who has conducted his readers over the two parallel routes\nwhich have just been marked out, will be brought to ask himself\nwhether he has been a sufficiently faithful guide and has not omitted\nto draw attention to all essential points in the regions passed\nthrough.\n\nOught we not to place by the side, or perhaps in front, of the authors\nwho have devised the practical appliances, those scholars who have\nconstructed the theories and realised the laboratory experiments of\nwhich, after all, the apparatus are only the immediate applications?\nIf we speak of the propagation of a current in a material medium, can\none forget the names of Fourier and of Ohm, who established by\ntheoretical considerations the laws which preside over this\npropagation? When one looks at the phenomena of induction, would it\nnot be just to remember that Arago foresaw them, and that Michael\nFaraday discovered them? It would be a delicate, and also a rather\npuerile task, to class men of genius in order of merit. The merit of\nan inventor like Edison and that of a theorist like Clerk Maxwell have\nno common measure, and mankind is indebted for its great progress to\nthe one as much as to the other.\n\nBefore relating how success attended the efforts to utilise electric\nwaves for the transmission of signals, we cannot without ingratitude\npass over in silence the theoretical speculations and the work of pure\nscience which led to the knowledge of these waves. It would therefore\nbe just, without going further back than Faraday, to say how that\nillustrious physicist drew attention to the part taken by insulating\nmedia in electrical phenomena, and to insist also on the admirable\nmemoirs in which for the first time Clerk Maxwell made a solid bridge\nbetween those two great chapters of Physics, optics and electricity,\nwhich till then had been independent of each other. And no doubt it\nwould be impossible not to evoke the memory of those who, by\nestablishing, on the other hand, the solid and magnificent structure\nof physical optics, and proving by their immortal works the undulatory\nnature of light, prepared from the opposite direction the future\nunity. In the history of the applications of electrical undulations,\nthe names of Young, Fresnel, Fizeau, and Foucault must be inscribed;\nwithout these scholars, the assimilation between electrical and\nluminous phenomena which they discovered and studied would evidently\nhave been impossible.\n\nSince there is an absolute identity of nature between the electric and\nthe luminous waves, we should, in all justice, also consider as\nprecursors those who devised the first luminous telegraphs. Claude\nChappe incontestably effected wireless telegraphy, thanks to the\nluminous ether, and the learned men, such as Colonel Mangin, who\nperfected optical telegraphy, indirectly suggested certain\nimprovements lately introduced into the present method.\n\nBut the physicist whose work should most of all be put in evidence is,\nwithout fear of contradiction, Heinrich Hertz. It was he who\ndemonstrated irrefutably, by experiments now classic, that an electric\ndischarge produces an undulatory disturbance in the ether contained in\nthe insulating media in its neighbourhood; it was he who, as a\nprofound theorist, a clever mathematician, and an experimenter of\nprodigious dexterity, made known the mechanism of the production, and\nfully elucidated that of the propagation of these electromagnetic\nwaves.\n\nHe must naturally himself have thought that his discoveries might be\napplied to the transmission of signals. It would appear, however, that\nwhen interrogated by a Munich engineer named Huber as to the\npossibility of utilising the waves for transmissions by telephone, he\nanswered in the negative, and dwelt on certain considerations relative\nto the difference between the periods of sounds and those of\nelectrical vibrations. This answer does not allow us to judge what\nmight have happened, had not a cruel death carried off in 1894, at the\nage of thirty-five, the great and unfortunate physicist.\n\nWe might also find in certain works earlier than the experiments of\nHertz attempts at transmission in which, unconsciously no doubt,\nphenomena were already set in operation which would, at this day, be\nclassed as electric oscillations. It is allowable no doubt, not to\nspeak of an American quack, Mahlon Loomis, who, according to Mr Story,\npatented in 1870 a project of communication in which he utilised the\nRocky Mountains on one side and Mont Blanc on the other, as gigantic\nantennae to establish communication across the Atlantic; but we cannot\npass over in silence the very remarkable researches of the American\nProfessor Dolbear, who showed, at the electrical exhibition of\nPhiladelphia in 1884, a set of apparatus enabling signals to be\ntransmitted at a distance, which he described as \"an exceptional\napplication of the principles of electrostatic induction.\" This\napparatus comprised groups of coils and condensers by means of which\nhe obtained, as we cannot now doubt, effects due to true electric\nwaves.\n\nPlace should also be made for a well-known inventor, D.E. Hughes, who\nfrom 1879 to 1886 followed up some very curious experiments in which\nalso these oscillations certainly played a considerable part. It was\nthis physicist who invented the microphone, and thus, in another way,\ndrew attention to the variations of contact resistance, a phenomenon\nnot far from that produced in the radio-conductors of Branly, which\nare important organs in the Marconi system. Unfortunately, fatigued\nand in ill-health, Hughes ceased his researches at the moment perhaps\nwhen they would have given him final results.\n\nIn an order of ideas different in appearance, but closely linked at\nbottom with the one just mentioned, must be recalled the discovery of\nradiophony in 1880 by Graham Bell, which was foreshadowed in 1875 by\nC.A. Brown. A luminous ray falling on a selenium cell produces a\nvariation of electric resistance, thanks to which a sound signal can\nbe transmitted by light. That delicate instrument the radiophone,\nconstructed on this principle, has wide analogies with the apparatus\nof to-day.\n\n\nSec. 6\n\nStarting from the experiments of Hertz, the history of wireless\ntelegraphy almost merges into that of the researches on electrical\nwaves. All the progress realised in the manner of producing and\nreceiving these waves necessarily helped to give rise to the\napplication already indicated. The experiments of Hertz, after being\nchecked in every laboratory, and having entered into the strong domain\nof our most certain knowledge, were about to yield the expected fruit.\n\nExperimenters like Sir Oliver Lodge in England, Righi in Italy,\nSarrazin and de la Rive in Switzerland, Blondlot in France, Lecher in\nGermany, Bose in India, Lebedeff in Russia, and theorists like M.H.\nPoincare and Professor Bjerknes, who devised ingenious arrangements or\nelucidated certain points left dark, are among the artisans of the\nwork which followed its natural evolution.\n\nIt was Professor R. Threlfall who seems to have been the first to\nclearly propose, in 1890, the application of the Hertzian waves to\ntelegraphy, but it was certainly Sir W. Crookes who, in a very\nremarkable article in the _Fortnightly Review_ of February 1892,\npointed out very clearly the road to be followed. He even showed in\nwhat conditions the Morse receiver might be applied to the new system\nof telegraphy.\n\nAbout the same period an American physicist, well known by his\ncelebrated experiments on high frequency currents--experiments, too,\nwhich are not unconnected with those on electric oscillations,--M.\nTesla, demonstrated that these oscillations could be transmitted to\nmore considerable distances by making use of two vertical antennae,\nterminated by large conductors.\n\nA little later, Sir Oliver Lodge succeeded, by the aid of the coherer,\nin detecting waves at relatively long distances, and Mr Rutherford\nobtained similar results with a magnetic indicator of his own\ninvention.\n\nAn important question of meteorology, the study of atmospheric\ndischarges, at this date led a few scholars, and more particularly the\nRussian, M. Popoff, to set up apparatus very analogous to the\nreceiving apparatus of the present wireless telegraphy. This comprised\na long antenna and filings-tube, and M. Popoff even pointed out that\nhis apparatus might well serve for the transmission of signals as soon\nas a generator of waves powerful enough had been discovered.\n\nFinally, on the 2nd June 1896, a young Italian, born in Bologna on the\n25th April 1874, Guglielmo Marconi, patented a system of wireless\ntelegraphy destined to become rapidly popular. Brought up in the\nlaboratory of Professor Righi, one of the physicists who had done most\nto confirm and extend the experiments of Hertz, Marconi had long been\nfamiliar with the properties of electric waves, and was well used to\ntheir manipulation. He afterwards had the good fortune to meet Sir\nWilliam (then Mr) Preece, who was to him an adviser of the highest\nauthority.\n\nIt has sometimes been said that the Marconi system contains nothing\noriginal; that the apparatus for producing the waves was the\noscillator of Righi, that the receiver was that employed for some two\nor three years by Professor Lodge and Mr Bose, and was founded on an\nearlier discovery by a French scholar, M. Branly; and, finally, that\nthe general arrangement was that established by M. Popoff.\n\nThe persons who thus rather summarily judge the work of M. Marconi\nshow a severity approaching injustice. It cannot, in truth, be denied\nthat the young scholar has brought a strictly personal contribution to\nthe solution of the problem he proposed to himself. Apart from his\nforerunners, and when their attempts were almost unknown, he had the\nvery great merit of adroitly arranging the most favourable\ncombination, and he was the first to succeed in obtaining practical\nresults, while he showed that the electric waves could be transmitted\nand received at distances enormous compared to those attained before\nhis day. Alluding to a well-known anecdote relating to Christopher\nColumbus, Sir W. Preece very justly said: \"The forerunners and rivals\nof Marconi no doubt knew of the eggs, but he it was who taught them to\nmake them stand on end.\" This judgment will, without any doubt, be the\none that history will definitely pronounce on the Italian scholar.\n\n\nSec. 7\n\nThe apparatus which enables the electric waves to be revealed, the\ndetector or indicator, is the most delicate organ in wireless\ntelegraphy. It is not necessary to employ as an indicator a\nfilings-tube or radio-conductor. One can, in principle, for the purpose\nof constructing a receiver, think of any one of the multiple effects\nproduced by the Hertzian waves. In many systems in use, and in the new\none of Marconi himself, the use of these tubes has been abandoned and\nreplaced by magnetic detectors.\n\nNevertheless, the first and the still most frequent successes are due\nto radio-conductors, and public opinion has not erred in attributing\nto the inventor of this ingenious apparatus a considerable and almost\npreponderant part in the invention of wave telegraphy.\n\nThe history of the discovery of radio-conductors is short, but it\ndeserves, from its importance, a chapter to itself in the history of\nwireless telegraphy. From a theoretical point of view, the phenomena\nproduced in those tubes should be set by the side of those studied by\nGraham Bell, C.A. Brown, and Summer Tainter, from the year 1878\nonward. The variations to which luminous waves give rise in the\nresistance of selenium and other substances are, doubtless, not\nunconnected with those which the electric waves produce in filings. A\nconnection can also be established between this effect of the waves\nand the variations of contact resistance which enabled Hughes to\nconstruct the microphone, that admirable instrument which is one of\nthe essential organs of telephony.\n\nMore directly, as an antecedent to the discovery, should be quoted the\nremark made by Varley in 1870, that coal-dust changes in conductivity\nwhen the electromotive force of the current which passes through it is\nmade to vary. But it was in 1884 that an Italian professor, Signor\nCalzecchi-Onesti, demonstrated in a series of remarkable experiments\nthat the metallic filings contained in a tube of insulating material,\ninto which two metallic electrodes are inserted, acquire a notable\nconductivity under different influences such as extra currents,\ninduced currents, sonorous vibrations, etc., and that this\nconductivity is easily destroyed; as, for instance, by turning the\ntube over and over.\n\nIn several memoirs published in 1890 and 1891, M. Ed. Branly\nindependently pointed out similar phenomena, and made a much more\ncomplete and systematic study of the question. He was the first to\nnote very clearly that the action described could be obtained by\nsimply making sparks pass in the neighbourhood of the radio-conductor,\nand that their great resistance could be restored to the filings by\ngiving a slight shake to the tube or to its supports.\n\nThe idea of utilising such a very interesting phenomenon as an\nindicator in the study of the Hertzian waves seems to have occurred\nsimultaneously to several physicists, among whom should be especially\nmentioned M. Ed. Branly himself, Sir Oliver Lodge, and MM. Le Royer\nand Van Beschem, and its use in laboratories rapidly became quite\ncommon.\n\nThe action of the waves on metallic powders has, however, remained\nsome what mysterious; for ten years it has been the subject of\nimportant researches by Professor Lodge, M. Branly, and a very great\nnumber of the most distinguished physicists. It is impossible to\nnotice here all these researches, but from a recent and very\ninteresting work of M. Blanc, it would seem that the phenomenon is\nallied to that of ionisation.\n\n\nSec. 8\n\nThe history of wireless telegraphy does not end with the first\nexperiments of Marconi; but from the moment their success was\nannounced in the public press, the question left the domain of pure\nscience to enter into that of commerce. The historian's task here\nbecomes different, but even more delicate; and he will encounter\ndifficulties which can be only known to one about to write the history\nof a commercial invention.\n\nThe actual improvements effected in the system are kept secret by the\nrival companies, and the most important results are patriotically left\nin darkness by the learned officers who operate discreetly in view of\nthe national defence. Meanwhile, men of business desirous of bringing\nout a company proclaim, with great nourish of advertisements, that\nthey are about to exploit a process superior to all others.\n\nOn this slippery ground the impartial historian must nevertheless\nventure; and he may not refuse to relate the progress accomplished,\nwhich is considerable. Therefore, after having described the\nexperiments carried out for nearly ten years by Marconi himself, first\nacross the Bristol Channel, then at Spezzia, between the coast and the\nironclad _San Bartolommeo_, and finally by means of gigantic apparatus\nbetween America and England, he must give the names of those who, in\nthe different civilised countries, have contributed to the improvement\nof the system of communication by waves; while he must describe what\nprecious services this system has already rendered to the art of war,\nand happily also to peaceful navigation.\n\nFrom the point of view of the theory of the phenomena, very remarkable\nresults have been obtained by various physicists, among whom should be\nparticularly mentioned M. Tissot, whose brilliant studies have thrown\na bright light on different interesting points, such as the role of\nthe antennae. It would be equally impossible to pass over in silence\nother recent attempts in a slightly different groove. Marconi's\nsystem, however improved it may be to-day, has one grave defect. The\nsynchronism of the two pieces of apparatus, the transmitter and the\nreceiver, is not perfect, so that a message sent off by one station\nmay be captured by some other station. The fact that the phenomena of\nresonance are not utilised, further prevents the quantity of energy\nreceived by the receiver from being considerable, and hence the\neffects reaped are very weak, so that the system remains somewhat\nfitful and the communications are often disturbed by atmospheric\nphenomena. Causes which render the air a momentary conductor, such as\nelectrical discharges, ionisation, etc., moreover naturally prevent\nthe waves from passing, the ether thus losing its elasticity.\n\nProfessor Ferdinand Braun of Strasburg has conceived the idea of\nemploying a mixed system, in which the earth and the water, which, as\nwe have seen, have often been utilised to conduct a current for\ntransmitting a signal, will serve as a sort of guide to the waves\nthemselves. The now well-known theory of the propagation of waves\nguided by a conductor enables it to be foreseen that, according to\ntheir periods, these waves will penetrate more or less deeply into the\nnatural medium, from which fact has been devised a method of\nseparating them according to their frequency. By applying this theory,\nM. Braun has carried out, first in the fortifications of Strasburg,\nand then between the island of Heligoland and the mainland,\nexperiments which have given remarkable results. We might mention also\nthe researches, in a somewhat analogous order of ideas, by an English\nengineer, Mr Armstrong, by Dr Lee de Forest, and also by Professor\nFessenden.\n\nHaving thus arrived at the end of this long journey, which has taken\nhim from the first attempts down to the most recent experiments, the\nhistorian can yet set up no other claim but that of having written the\ncommencement of a history which others must continue in the future.\nProgress does not stop, and it is never permissible to say that an\ninvention has reached its final form.\n\nShould the historian desire to give a conclusion to his labour and\nanswer the question the reader would doubtless not fail to put to him,\n\"To whom, in short, should the invention of wireless telegraphy more\nparticularly be attributed?\" he should certainly first give the name\nof Hertz, the genius who discovered the waves, then that of Marconi,\nwho was the first to transmit signals by the use of Hertzian\nundulations, and should add those of the scholars who, like Morse,\nPopoff, Sir W. Preece, Lodge, and, above all, Branly, have devised the\narrangements necessary for their transmission. But he might then\nrecall what Voltaire wrote in the _Philosophical Dictionary_:\n\n\"What! We wish to know what was the exact theology of Thot, of\nZerdust, of Sanchuniathon, of the first Brahmins, and we are ignorant\nof the inventor of the shuttle! The first weaver, the first mason, the\nfirst smith, were no doubt great geniuses, but they were disregarded.\nWhy? Because none of them invented a perfected art. The one who\nhollowed out an oak to cross a river never made a galley; those who\npiled up rough stones with girders of wood did not plan the Pyramids.\nEverything is made by degrees and the glory belongs to no one.\"\n\nTo-day, more than ever, the words of Voltaire are true: science\nbecomes more and more impersonal, and she teaches us that progress is\nnearly always due to the united efforts of a crowd of workers, and is\nthus the best school of social solidarity.\n\n\n\n\nCHAPTER VIII\n\nTHE CONDUCTIVITY OF GASES AND THE IONS\n\n\nSec. 1. THE CONDUCTIVITY OF GASES\n\nIf we were confined to the facts I have set forth above, we might\nconclude that two classes of phenomena are to-day being interpreted\nwith increasing correctness in spite of the few difficulties which\nhave been pointed out. The hypothesis of the molecular constitution of\nmatter enables us to group together one of these classes, and the\nhypothesis of the ether leads us to co-ordinate the other.\n\nBut these two classes of phenomena cannot be considered independent of\neach other. Relations evidently exist between matter and the ether,\nwhich manifest themselves in many cases accessible to experiment, and\nthe search for these relations appears to be the paramount problem the\nphysicist should set himself. The question has, for a long time, been\nattacked on various sides, but the recent discoveries in the\nconductivity of gases, of the radioactive substances, and of the\ncathode and similar rays, have allowed us of late years to regard it\nin a new light. Without wishing to set out here in detail facts which\nfor the most part are well known, we will endeavour to group the chief\nof them round a few essential ideas, and will seek to state precisely\nthe data they afford us for the solution of this grave problem.\n\nIt was the study of the conductivity of gases which at the very first\nfurnished the most important information, and allowed us to penetrate\nmore deeply than had till then been possible into the inmost\nconstitution of matter, and thus to, as it were, catch in the act the\nactions that matter can exercise on the ether, or, reciprocally, those\nit may receive from it.\n\nIt might, perhaps, have been foreseen that such a study would prove\nremarkably fruitful. The examination of the phenomena of electrolysis\nhad, in fact, led to results of the highest importance on the\nconstitution of liquids, and the gaseous media which presented\nthemselves as particularly simple in all their properties ought, it\nwould seem, to have supplied from the very first a field of\ninvestigation easy to work and highly productive.\n\nThis, however, was not at all the case. Experimental complications\nspringing up at every step obscured the problem. One generally found\none's self in the presence of violent disruptive discharges with a\ntrain of accessory phenomena, due, for instance, to the use of\nmetallic electrodes, and made evident by the complex appearance of\naigrettes and effluves; or else one had to deal with heated gases\ndifficult to handle, which were confined in receptacles whose walls\nplayed a troublesome part and succeeded in veiling the simplicity of\nthe fundamental facts. Notwithstanding, therefore, the efforts of a\ngreat number of seekers, no general idea disengaged itself out of a\nmass of often contradictory information.\n\nMany physicists, in France particularly, discarded the study of\nquestions which seemed so confused, and it must even be frankly\nacknowledged that some among them had a really unfounded distrust of\ncertain results which should have been considered proved, but which\nhad the misfortune to be in contradiction with the theories in current\nuse. All the classic ideas relating to electrical phenomena led to the\nconsideration that there existed a perfect symmetry between the two\nelectricities, positive and negative. In the passing of electricity\nthrough gases there is manifested, on the contrary, an evident\ndissymmetry. The anode and the cathode are immediately distinguished\nin a tube of rarefied gas by their peculiar appearance; and the\nconductivity does not appear, under certain conditions, to be the same\nfor the two modes of electrification.\n\nIt is not devoid of interest to note that Erman, a German scholar,\nonce very celebrated and now generally forgotten, drew attention as\nearly as 1815 to the unipolar conductivity of a flame. His\ncontemporaries, as may be gathered from the perusal of the treatises\non physics of that period, attached great importance to this\ndiscovery; but, as it was somewhat inconvenient and did not readily\nfit in with ordinary studies, it was in due course neglected, then\nconsidered as insufficiently established, and finally wholly\nforgotten.\n\nAll these somewhat obscure facts, and some others--such as the\ndifferent action of ultra-violet radiations on positively and\nnegatively charged bodies--are now, on the contrary, about to be\nco-ordinated, thanks to the modern ideas on the mechanism of conduction;\nwhile these ideas will also allow us to interpret the most striking\ndissymmetry of all, i.e. that revealed by electrolysis itself, a\ndissymmetry which certainly can not be denied, but to which sufficient\nattention has not been given.\n\nIt is to a German physicist, Giese, that we owe the first notions on\nthe mechanism of the conductivity of gases, as we now conceive it. In\ntwo memoirs published in 1882 and 1889, he plainly arrives at the\nconception that conduction in gases is not due to their molecules, but\nto certain fragments of them or to ions. Giese was a forerunner, but\nhis ideas could not triumph so long as there were no means of\nobserving conduction in simple circumstances. But this means has now\nbeen supplied in the discovery of the X rays. Suppose we pass through\nsome gas at ordinary pressure, such as hydrogen, a pencil of X rays.\nThe gas, which till then has behaved as a perfect insulator,[29]\nsuddenly acquires a remarkable conductivity. If into this hydrogen two\nmetallic electrodes in communication with the two poles of a battery\nare introduced, a current is set up in very special conditions which\nremind us, when they are checked by experiments, of the mechanism\nwhich allows the passage of electricity in electrolysis, and which is\nso well represented to us when we picture to ourselves this passage as\ndue to the migration towards the electrodes, under the action of the\nfield, of the two sets of ions produced by the spontaneous division of\nthe molecule within the solution.\n\n[Footnote 29: At least, so long as it is not introduced between the\ntwo coatings of a condenser having a difference of potential\nsufficient to overcome what M. Bouty calls its dielectric cohesion. We\nleave on one side this phenomenon, regarding which M. Bouty has\narrived at extremely important results by a very remarkable series of\nexperiments; but this question rightly belongs to a special study of\nelectrical phenomena which is not yet written.]\n\nLet us therefore recognise with J.J. Thomson and the many physicists\nwho, in his wake, have taken up and developed the idea of Giese, that,\nunder the influence of the X rays, for reasons which will have to be\ndetermined later, certain gaseous molecules have become divided into\ntwo portions, the one positively and the other negatively electrified,\nwhich we will call, by analogy with the kindred phenomenon in\nelectrolysis, by the name of ions. If the gas be then placed in an\nelectric field, produced, for instance, by two metallic plates\nconnected with the two poles of a battery respectively, the positive\nions will travel towards the plate connected with the negative pole,\nand the negative ions in the contrary direction. There is thus\nproduced a current due to the transport to the electrodes of the\ncharges which existed on the ions.\n\nIf the gas thus ionised be left to itself, in the absence of any\nelectric field, the ions, yielding to their mutual attraction, must\nfinally meet, combine, and reconstitute a neutral molecule, thus\nreturning to their initial condition. The gas in a short while loses\nthe conductivity which it had acquired; or this is, at least, the\nphenomenon at ordinary temperatures. But if the temperature is raised,\nthe relative speeds of the ions at the moment of impact may be great\nenough to render it impossible for the recombination to be produced in\nits entirety, and part of the conductivity will remain.\n\nEvery element of volume rendered a conductor therefore furnishes, in\nan electric field, equal quantities of positive and negative\nelectricity. If we admit, as mentioned above, that these liberated\nquantities are borne by ions each bearing an equal charge, the number\nof these ions will be proportional to the quantity of electricity, and\ninstead of speaking of a quantity of electricity, we could use the\nequivalent term of number of ions. For the excitement produced by a\ngiven pencil of X rays, the number of ions liberated will be fixed.\nThus, from a given volume of gas there can only be extracted an\nequally determinate quantity of electricity.\n\nThe conductivity produced is not governed by Ohm's law. The intensity\nis not proportional to the electromotive force, and it increases at\nfirst as the electromotive force augments; but it approaches\nasymptotically to a maximum value which corresponds to the number of\nions liberated, and can therefore serve as a measure of the power of\nthe excitement. It is this current which is termed the _current of\nsaturation_.\n\nM. Righi has ably demonstrated that ionised gas does not obey the law\nof Ohm by an experiment very paradoxical in appearance. He found that,\nthe greater the distance of the two electrode plates from each, the\ngreater may be, within certain limits, the intensity of the current.\nThe fact is very clearly interpreted by the theory of ionisation,\nsince the greater the length of the gaseous column the greater must be\nthe number of ions liberated.\n\nOne of the most striking characteristics of ionised gases is that of\ndischarging electrified conductors. This phenomenon is not produced by\nthe departure of the charge that these conductors may possess, but by\nthe advent of opposite charges brought to them by ions which obey the\nelectrostatic attraction and abandon their own electrification when\nthey come in contact with these conductors.\n\nThis mode of regarding the phenomena is extremely convenient and\neminently suggestive. It may, no doubt, be thought that the image of\nthe ions is not identical with objective reality, but we are compelled\nto acknowledge that it represents with absolute faithfulness all the\ndetails of the phenomena.\n\nOther facts, moreover, will give to this hypothesis a still greater\nvalue; we shall even be able, so to speak, to grasp these ions\nindividually, to count them, and to measure their charge.\n\n\nSec. 2. THE CONDENSATION OF WATER-VAPOUR BY IONS\n\nIf the pressure of a vapour--that of water, for instance--in the\natmosphere reaches the value of the maximum pressure corresponding to\nthe temperature of the experiment, the elementary theory teaches us\nthat the slightest decrease in temperature will induce a condensation;\nthat small drops will form, and the mist will turn into rain.\n\nIn reality, matters do not occur in so simple a manner. A more or\nless considerable delay may take place, and the vapour will remain\nsupersaturated. We easily discover that this phenomenon is due\nto the intervention of capillary action. On a drop of liquid a\nsurface-tension takes effect which gives rise to a pressure which\nbecomes greater the smaller the diameter of the drop.\n\nPressure facilitates evaporation, and on more closely examining this\nreaction we arrive at the conclusion that vapour can never\nspontaneously condense itself when liquid drops already formed are not\npresent, unless forces of another nature intervene to diminish the\neffect of the capillary forces. In the most frequent cases, these\nforces come from the dust which is always in suspension in the air, or\nwhich exists in any recipient. Grains of dust act by reason of their\nhygrometrical power, and form germs round which drops presently form.\nIt is possible to make use, as did M. Coulier as early as 1875, of\nthis phenomenon to carry off the germs of condensation, by producing\nby expansion in a bottle containing a little water a preliminary mist\nwhich purifies the air. In subsequent experiments it will be found\nalmost impossible to produce further condensation of vapour.\n\nBut these forces may also be of electrical origin. Von Helmholtz long\nsince showed that electricity exercises an influence on the\ncondensation of the vapour of water, and Mr C.T.R. Wilson, with this\nview, has made truly quantitative experiments. It was rapidly\ndiscovered after the apparition of the X rays that gases that have\nbecome conductors, that is, ionised gases, also facilitate the\ncondensation of supersaturated water vapour.\n\nWe are thus led by a new road to the belief that electrified centres\nexist in gases, and that each centre draws to itself the neighbouring\nmolecules of water, as an electrified rod of resin does the light\nbodies around it. There is produced in this manner round each ion an\nassemblage of molecules of water which constitute a germ capable of\ncausing the formation of a drop of water out of the condensation of\nexcess vapour in the ambient air. As might be expected, the drops are\nelectrified, and take to themselves the charge of the centres round\nwhich they are formed; moreover, as many drops are created as there\nare ions. Thereafter we have only to count these drops to ascertain\nthe number of ions which existed in the gaseous mass.\n\nTo effect this counting, several methods have been used, differing in\nprinciple but leading to similar results. It is possible, as Mr C.T.R.\nWilson and Professor J.J. Thomson have done, to estimate, on the one\nhand, the weight of the mist which is produced in determined\nconditions, and on the other, the average weight of the drops,\naccording to the formula formerly given by Sir G. Stokes, by deducting\ntheir diameter from the speed with which this mist falls; or we can,\nwith Professor Lemme, determine the average radius of the drops by an\noptical process, viz. by measuring the diameter of the first\ndiffraction ring produced when looking through the mist at a point of\nlight.\n\nWe thus get to a very high number. There are, for instance, some\ntwenty million ions per centimetre cube when the rays have produced\ntheir maximum effect, but high as this figure is, it is still very\nsmall compared with the total number of molecules. All conclusions\ndrawn from kinetic theory lead us to think that in the same space\nthere must exist, by the side of a molecule divided into two ions, a\nthousand millions remaining in a neutral state and intact.\n\nMr C.T.R. Wilson has remarked that the positive and negative ions do\nnot produce condensation with the same facility. The ions of a\ncontrary sign may be almost completely separated by placing the\nionised gas in a suitably disposed field. In the neighbourhood of a\nnegative disk there remain hardly any but positive ions, and against a\npositive disk none but negative; and in effecting a separation of this\nkind, it will be noticed that condensation by negative ions is easier\nthan by the positive.\n\nIt is, consequently, possible to cause condensation on negative\ncentres only, and to study separately the phenomena produced by the\ntwo kinds of ions. It can thus be verified that they really bear\ncharges equal in absolute value, and these charges can even be\nestimated, since we already know the number of drops. This estimate\ncan be made, for example, by comparing the speed of the fall of a mist\nin fields of different values, or, as did J.J. Thomson, by measuring\nthe total quantity of electricity liberated throughout the gas.\n\nAt the degree of approximation which such experiments imply, we find\nthat the charge of a drop, and consequently the charge borne by an\nion, is sensibly 3.4 x 10^{-10} electrostatic or 1.1 x 10^{-20}\nelectromagnetic units. This charge is very near that which the study\nof the phenomena of ordinary electrolysis leads us to attribute to a\nunivalent atom produced by electrolytic dissociation.\n\nSuch a coincidence is evidently very striking; but it will not be the\nonly one, for whatever phenomenon be studied it will always appear\nthat the smallest charge we can conceive as isolated is that\nmentioned. We are, in fact, in presence of a natural unit, or, if you\nwill, of an atom of electricity.\n\nWe must, however, guard against the belief that the gaseous ion is\nidentical with the electrolytic ion. Sensible differences between\nthose are immediately apparent, and still greater ones will be\ndiscovered on closer examination.\n\nAs M. Perrin has shown, the ionisation produced by the X-rays in no\nway depends on the chemical composition of the gas; and whether we\ntake a volume of gaseous hydrochloric acid or a mixture of hydrogen\nand chlorine in the same condition, all the results will be identical:\nand chemical affinities play no part here.\n\nWe can also obtain other information regarding ions: we can ascertain,\nfor instance, their velocities, and also get an idea of their order of\nmagnitude.\n\nBy treating the speeds possessed by the liberated charges as\ncomponents of the known speed of a gaseous current, Mr Zeleny measures\nthe mobilities, that is to say, the speeds acquired by the positive\nand negative charges in a field equal to the electrostatic unit. He\nhas thus found that these mobilities are different, and that they\nvary, for example, between 400 and 200 centimetres per second for the\ntwo charges in dry gases, the positive being less mobile than the\nnegative ions, which suggests the idea that they are of greater\nmass.[30]\n\n[Footnote 30: A full account of these experiments, which were executed\nat the Cavendish Laboratory, is to be found in _Philosophical\nTransactions_, A., vol. cxcv. (1901), pp. 193 et seq.--ED.]\n\nM. Langevin, who has made himself the eloquent apostle of the new\ndoctrines in France, and has done much to make them understood and\nadmitted, has personally undertaken experiments analogous to those of\nM. Zeleny, but much more complete. He has studied in a very ingenious\nmanner, not only the mobilities, but also the law of recombination\nwhich regulates the spontaneous return of the gas to its normal state.\nHe has determined experimentally the relation of the number of\nrecombinations to the number of collisions between two ions of\ncontrary sign, by studying the variation produced by a change in the\nvalue of the field, in the quantity of electricity which can be\ncollected in the gas separating two parallel metallic plates, after\nthe passage through it for a very short time of the Roentgen rays\nemitted during one discharge of a Crookes tube. If the image of the\nions is indeed conformable to reality, this relation must evidently\nalways be smaller than unity, and must tend towards this value when\nthe mobility of the ions diminishes, that is to say, when the pressure\nof the gas increases. The results obtained are in perfect accord with\nthis anticipation.\n\nOn the other hand, M. Langevin has succeeded, by following the\ndisplacement of the ions between the parallel plates after the\nionisation produced by the radiation, in determining the absolute\nvalues of the mobilities with great precision, and has thus clearly\nplaced in evidence the irregularity of the mobilities of the positive\nand negative ions respectively. Their mass can be calculated when we\nknow, through experiments of this kind, the speed of the ions in a\ngiven field, and on the other hand--as we can now estimate their\nelectric charge--the force which moves them. They evidently progress\nmore slowly the larger they are; and in the viscous medium constituted\nby the gas, the displacement is effected at a speed sensibly\nproportional to the motive power.\n\nAt the ordinary temperature these masses are relatively considerable,\nand are greater for the positive than for the negative ions, that is\nto say, they are about the order of some ten molecules. The ions,\ntherefore, seem to be formed by an agglomeration of neutral molecules\nmaintained round an electrified centre by electrostatic attraction. If\nthe temperature rises, the thermal agitation will become great enough\nto prevent the molecules from remaining linked to the centre. By\nmeasurements effected on the gases of flames, we arrive at very\ndifferent values of the masses from those found for ordinary ions, and\nabove all, very different ones for ions of contrary sign. The negative\nions have much more considerable velocities than the positive ones.\nThe latter also seem to be of the same size as atoms; and the\nfirst-named must, consequently, be considered as very much smaller,\nand probably about a thousand times less.\n\nThus, for the first time in science, the idea appears that the atom is\nnot the smallest fraction of matter to be considered. Fragments a\nthousand times smaller may exist which possess, however, a negative\ncharge. These are the electrons, which other considerations will again\nbring to our notice.\n\n\nSec. 3. HOW IONS ARE PRODUCED\n\nIt is very seldom that a gaseous mass does not contain a few ions.\nThey may have been formed from many causes, for although to give\nprecision to our studies, and to deal with a well ascertained case, I\nmentioned only ionisation by the X rays in the first instance, I ought\nnot to give the impression that the phenomenon is confined to these\nrays. It is, on the contrary, very general, and ionisation is just as\nwell produced by the cathode rays, by the radiations emitted by\nradio-active bodies, by the ultra-violet rays, by heating to a high\ntemperature, by certain chemical actions, and finally by the impact of\nthe ions already existing in neutral molecules.\n\nOf late years these new questions have been the object of a multitude\nof researches, and if it has not always been possible to avoid some\nconfusion, yet certain general conclusions may be drawn. The\nionisation by flames, in particular, is fairly well known. For it to\nbe produced spontaneously, it would appear that there must exist\nsimultaneously a rather high temperature and a chemical action in the\ngas. According to M. Moreau, the ionisation is very marked when the\nflame contains the vapour of the salt of an alkali or of an alkaline\nearth, but much less so when it contains that of other salts.\nArrhenius, Mr C.T.R. Wilson, and M. Moreau, have studied all the\ncircumstances of the phenomenon; and it seems indeed that there is a\nsomewhat close analogy between what first occurs in the saline vapours\nand that which is noted in liquid electrolytes. There should be\nproduced, as soon as a certain temperature is reached, a dissociation\nof the saline molecule; and, as M. Moreau has shown in a series of\nvery well conducted researches, the ions formed at about 100 deg.C. seem\nconstituted by an electrified centre of the size of a gas molecule,\nsurrounded by some ten layers of other molecules. We are thus dealing\nwith rather large ions, but according to Mr Wilson, this condensation\nphenomenon does not affect the number of ions produced by\ndissociation. In proportion as the temperature rises, the molecules\ncondensed round the nucleus disappear, and, as in all other\ncircumstances, the negative ion tends to become an electron, while the\npositive ion continues the size of an atom.\n\nIn other cases, ions are found still larger than those of saline\nvapours, as, for example, those produced by phosphorus. It has long\nbeen known that air in the neighbourhood of phosphorus becomes a\nconductor, and the fact, pointed out as far back as 1885 by Matteucci,\nhas been well studied by various experimenters, by MM. Elster and\nGeitel in 1890, for instance. On the other hand, in 1893 Mr Barus\nestablished that the approach of a stick of phosphorus brings about\nthe condensation of water vapour, and we really have before us,\ntherefore, in this instance, an ionisation. M. Bloch has succeeded in\ndisentangling the phenomena, which are here very complex, and in\nshowing that the ions produced are of considerable dimensions; for\ntheir speed in the same conditions is on the average a thousand times\nless than that of ions due to the X rays. M. Bloch has established\nalso that the conductivity of recently-prepared gases, already studied\nby several authors, was analogous to that which is produced by\nphosphorus, and that it is intimately connected with the presence of\nthe very tenuous solid or liquid dust which these gases carry with\nthem, while the ions are of the same order of magnitude. These large\nions exist, moreover, in small quantities in the atmosphere; and M.\nLangevin lately succeeded in revealing their presence.\n\nIt may happen, and this not without singularly complicating matters,\nthat the ions which were in the midst of material molecules produce,\nas the result of collisions, new divisions in these last. Other ions\nare thus born, and this production is in part compensated for by\nrecombinations between ions of opposite signs. The impacts will be\nmore active in the event of the gas being placed in a field of force\nand of the pressure being slight, the speed attained being then\ngreater and allowing the active force to reach a high value. The\nenergy necessary for the production of an ion is, in fact, according\nto Professor Rutherford and Professor Stark, something considerable,\nand it much exceeds the analogous force in electrolytic decomposition.\n\nIt is therefore in tubes of rarefied gas that this ionisation by\nimpact will be particularly felt. This gives us the reason for the\naspect presented by Geissler tubes. Generally, in the case of\ndischarges, new ions produced by the molecules struck come to add\nthemselves to the electrons produced, as will be seen, by the cathode.\nA full discussion has led to the interpretation of all the known\nfacts, and to our understanding, for instance, why there exist bright\nor dark spaces in certain regions of the tube. M. Pellat, in\nparticular, has given some very fine examples of this concordance\nbetween the theory and the facts he has skilfully observed.\n\nIn all the circumstances, then, in which ions appear, their formation\nhas doubtless been provoked by a mechanism analogous to that of the\nshock. The X rays, if they are attributable to sudden variations in\nthe ether--that is to say, a variation of the two vectors of Hertz--\nthemselves produce within the atom a kind of electric impulse which\nbreaks it into two electrified fragments; _i.e._ the positive centre,\nthe size of the molecule itself, and the negative centre, constituted\nby an electron a thousand times smaller. Round these two centres, at\nthe ordinary temperature, are agglomerated by attraction other\nmolecules, and in this manner the ions whose properties have just been\nstudied are formed.\n\n\nSec. 4. ELECTRONS IN METALS\n\nThe success of the ionic hypothesis as an interpretation of the\nconductivity of electrolytes and gases has suggested the desire to try\nif a similar hypothesis can represent the ordinary conductivity of\nmetals. We are thus led to conceptions which at first sight seem\naudacious because they are contrary to our habits of mind. They must\nnot, however, be rejected on that account. Electrolytic dissociation\nat first certainly appeared at least as strange; yet it has ended by\nforcing itself upon us, and we could, at the present day, hardly\ndispense with the image it presents to us.\n\nThe idea that the conductivity of metals is not essentially different\nfrom that of electrolytic liquids or gases, in the sense that the\npassage of the current is connected with the transport of small\nelectrified particles, is already of old date. It was enunciated by W.\nWeber, and afterwards developed by Giese, but has only obtained its\ntrue scope through the effect of recent discoveries. It was the\nresearches of Riecke, later, of Drude, and, above all, those of J.J.\nThomson, which have allowed it to assume an acceptable form. All these\nattempts are connected however with the general theory of Lorentz,\nwhich we will examine later.\n\nIt will be admitted that metallic atoms can, like the saline molecule\nin a solution, partially dissociate themselves. Electrons, very much\nsmaller than atoms, can move through the structure, considerable to\nthem, which is constituted by the atom from which they have just been\ndetached. They may be compared to the molecules of a gas which is\nenclosed in a porous body. In ordinary conditions, notwithstanding the\ngreat speed with which they are animated, they are unable to travel\nlong distances, because they quickly find their road barred by a\nmaterial atom. They have to undergo innumerable impacts, which throw\nthem first in one direction and then in another. The passage of a\ncurrent is a sort of flow of these electrons in a determined\ndirection. This electric flow brings, however, no modification to the\nmaterial medium traversed, since every electron which disappears at\nany point is replaced by another which appears at once, and in all\nmetals the electrons are identical.\n\nThis hypothesis leads us to anticipate certain facts which experience\nconfirms. Thus J.J. Thomson shows that if, in certain conditions, a\nconductor is placed in a magnetic field, the ions have to describe an\nepicycloid, and their journey is thus lengthened, while the electric\nresistance must increase. If the field is in the direction of the\ndisplacement, they describe helices round the lines of force and the\nresistance is again augmented, but in different proportions. Various\nexperimenters have noted phenomena of this kind in different\nsubstances.\n\nFor a long time it has been noticed that a relation exists between the\ncalorific and the electric conductivity; the relation of these two\nconductivities is sensibly the same for all metals. The modern theory\ntends to show simply that it must indeed be so. Calorific conductivity\nis due, in fact, to an exchange of electrons between the hot and the\ncold regions, the heated electrons having the greater velocity, and\nconsequently the more considerable energy. The calorific exchanges\nthen obey laws similar to those which govern electric exchanges; and\ncalculation even leads to the exact values which the measurements have\ngiven.[31]\n\n[Footnote 31: The whole of this argument is brilliantly set forth by\nProfessor Lorentz in a lecture delivered to the Electrotechnikerverein\nat Berlin in December 1904, and reprinted, with additions, in the\n_Archives Neerlandaises_ of 1906.--ED.]\n\nIn the same way Professor Hesehus has explained how contact\nelectrification is produced, by the tendency of bodies to equalise\ntheir superficial properties by means of a transport of electrons, and\nMr Jeans has shown that we should discover the existence of the\nwell-known laws of distribution over conducting bodies in electrostatic\nequilibrium. A metal can, in fact, be electrified, that is to say, may\npossess an excess of positive or negative electrons which cannot\neasily leave it in ordinary conditions. To cause them to do so would\nneed an appreciable amount of work, on account of the enormous\ndifference of the specific inductive capacities of the metal and of\nthe insulating medium in which it is plunged.\n\nElectrons, however, which, on arriving at the surface of the metal,\npossessed a kinetic energy superior to this work, might be shot forth\nand would be disengaged as a vapour escapes from a liquid. Now, the\nnumber of these rapid electrons, at first very slight, increases,\naccording to the kinetic theory, when the temperature rises, and\ntherefore we must reckon that a wire, on being heated, gives out\nelectrons, that is to say, loses negative electricity and sends into\nthe surrounding media electrified centres capable of producing the\nphenomena of ionisation. Edison, in 1884, showed that from the\nfilament of an incandescent lamp there escaped negative electric\ncharges. Since then, Richardson and J.J. Thomson have examined\nanalogous phenomena. This emission is a very general phenomenon which,\nno doubt, plays a considerable part in cosmic physics. Professor\nArrhenius explains, for instance, the polar auroras by the action of\nsimilar corpuscules emitted by the sun.\n\nIn other phenomena we seem indeed to be confronted by an emission, not\nof negative electrons, but of positive ions. Thus, when a wire is\nheated, not _in vacuo_, but in a gas, this wire begins to electrify\nneighbouring bodies positively. J.J. Thomson has measured the mass of\nthese positive ions and finds it considerable, i.e. about 150 times\nthat of an atom of hydrogen. Some are even larger, and constitute\nalmost a real grain of dust. We here doubtless meet with the phenomena\nof disaggregation undergone by metals at a red heat.\n\n\n\n\nCHAPTER IX\n\nCATHODE RAYS AND RADIOACTIVE BODIES\n\n\nSec. 1. THE CATHODE RAYS\n\nA wire traversed by an electric current is, as has just been\nexplained, the seat of a movement of electrons. If we cut this wire, a\nflood of electrons, like a current of water which, at the point where\na pipe bursts, flows out in abundance, will appear to spring out\nbetween the two ends of the break.\n\nIf the energy of the electrons is sufficient, these electrons will in\nfact rush forth and be propagated in the air or in the insulating\nmedium interposed; but the phenomena of the discharge will in general\nbe very complex. We shall here only examine a particularly simple\ncase, viz., that of the cathode rays; and without entering into\ndetails, we shall only note the results relating to these rays which\nfurnish valuable arguments in favour of the electronic hypothesis and\nsupply solid materials for the construction of new theories of\nelectricity and matter.\n\nFor a long time it was noticed that the phenomena in a Geissler tube\nchanged their aspect considerably, when the gas pressure became very\nweak, without, however, a complete vacuum being formed. From the\ncathode there is shot forth normally and in a straight line a flood\nwithin the tube, dark but capable of impressing a photographic plate,\nof developing the fluorescence of various substances (particularly the\nglass walls of the tube), and of producing calorific and mechanical\neffects. These are the cathode rays, so named in 1883 by E. Wiedemann,\nand their name, which was unknown to a great number of physicists till\nbarely twelve years ago, has become popular at the present day.\n\nAbout 1869, Hittorf made an already very complete study of them and\nput in evidence their principal properties; but it was the researches\nof Sir W. Crookes in especial which drew attention to them. The\ncelebrated physicist foresaw that the phenomena which were thus\nproduced in rarefied gases were, in spite of their very great\ncomplication, more simple than those presented by matter under the\nconditions in which it is generally met with.\n\nHe devised a celebrated theory no longer admissible in its entirety,\nbecause it is not in complete accord with the facts, which was,\nhowever, very interesting, and contained, in germ, certain of our\npresent ideas. In the opinion of Crookes, in a tube in which the gas\nhas been rarefied we are in presence of a special state of matter. The\nnumber of the gas molecules has become small enough for their\nindependence to be almost absolute, and they are able in this\nso-called radiant state to traverse long spaces without departing\nfrom a straight line. The cathode rays are due to a kind of molecular\nbombardment of the walls of the tubes, and of the screens which can be\nintroduced into them; and it is the molecules, electrified by their\ncontact with the cathode and then forcibly repelled by electrostatic\naction, which produce, by their movement and their _vis viva_, all the\nphenomena observed. Moreover, these electrified molecules animated\nwith extremely rapid velocities correspond, according to the theory\nverified in the celebrated experiment of Rowland on convection\ncurrents, to a true electric current, and can be deviated by a magnet.\n\nNotwithstanding the success of Crookes' experiments, many physicists--\nthe Germans especially--did not abandon an hypothesis entirely\ndifferent from that of radiant matter. They continued to regard the\ncathode radiation as due to particular radiations of a nature still\nlittle known but produced in the luminous ether. This interpretation\nseemed, indeed, in 1894, destined to triumph definitely through the\nremarkable discovery of Lenard, a discovery which, in its turn, was to\nprovoke so many others and to bring about consequences of which the\nimportance seems every day more considerable.\n\nProfessor Lenard's fundamental idea was to study the cathode rays\nunder conditions different from those in which they are produced.\nThese rays are born in a very rarefied space, under conditions\nperfectly determined by Sir W. Crookes; but it was a question whether,\nwhen once produced, they would be capable of propagating themselves in\nother media, such as a gas at ordinary pressure, or even in an\nabsolute vacuum. Experiment alone could answer this question, but\nthere were difficulties in the way of this which seemed almost\ninsurmountable. The rays are stopped by glass even of slight\nthickness, and how then could the almost vacuous space in which they\nhave to come into existence be separated from the space, absolutely\nvacuous or filled with gas, into which it was desired to bring them?\n\nThe artifice used was suggested to Professor Lenard by an experiment\nof Hertz. The great physicist had, in fact, shortly before his\npremature death, taken up this important question of the cathode rays,\nand his genius left there, as elsewhere, its powerful impress. He had\nshown that metallic plates of very slight thickness were transparent\nto the cathode rays; and Professor Lenard succeeded in obtaining\nplates impermeable to air, but which yet allowed the pencil of cathode\nrays to pass through them.\n\nNow if we take a Crookes tube with the extremity hermetically closed\nby a metallic plate with a slit across the diameter of 1 mm. in width,\nand stop this slit with a sheet of very thin aluminium, it will be\nimmediately noticed that the rays pass through the aluminium and pass\noutside the tube. They are propagated in air at atmospheric pressure,\nand they can also penetrate into an absolute vacuum. They therefore\ncan no longer be attributed to radiant matter, and we are led to think\nthat the energy brought into play in this phenomenon must have its\nseat in the light-bearing ether itself.\n\nBut it is a very strange light which is thus subject to magnetic\naction, which does not obey the principle of equal angles, and for\nwhich the most various gases are already disturbed media. According to\nCrookes it possesses also the singular property of carrying with it\nelectric charges.\n\nThis convection of negative electricity by the cathode rays seems\nquite inexplicable on the hypothesis that the rays are ethereal\nradiations. Nothing then remained in order to maintain this\nhypothesis, except to deny the convection, which, besides, was only\nestablished by indirect experiments. That the reality of this\ntransport has been placed beyond dispute by means of an extremely\nelegant experiment which is all the more convincing that it is so very\nsimple, is due to M. Perrin. In the interior of a Crookes tube he\ncollected a pencil of cathode rays in a metal cylinder. According to\nthe elementary principles of electricity the cylinder must become\ncharged with the whole charge, if there be one, brought to it by the\nrays, and naturally various precautions had to be taken. But the\nresult was very precise, and doubt could no longer exist--the rays\nwere electrified.\n\nIt might have been, and indeed was, maintained, some time after this\nexperiment was published, that while the phenomena were complex inside\nthe tube, outside, things might perhaps occur differently. Lenard\nhimself, however, with that absence of even involuntary prejudice\ncommon to all great minds, undertook to demonstrate that the opinion\nhe at first held could no longer be accepted, and succeeded in\nrepeating the experiment of M. Perrin on cathode rays in the air and\neven _in vacuo_.\n\nOn the wrecks of the two contradictory hypotheses thus destroyed, and\nout of the materials from which they had been built, a theory has been\nconstructed which co-ordinates all the known facts. This theory is\nfurthermore closely allied to the theory of ionisation, and, like this\nlatter, is based on the concept of the electron. Cathode rays are\nelectrons in rapid motion.\n\nThe phenomena produced both inside and outside a Crookes tube are,\nhowever, generally complex. In Lenard's first experiments, and in many\nothers effected later when this region of physics was still very\nlittle known, a few confusions may be noticed even at the present day.\n\nAt the spot where the cathode rays strike the walls of the tube the\nessentially different X rays appear. These differ from the cathode\nradiations by being neither electrified nor deviated by a magnet. In\ntheir turn these X rays may give birth to the secondary rays of M.\nSagnac; and often we find ourselves in presence of effects from these\nlast-named radiations and not from the true cathode rays.\n\nThe electrons, when they are propagated in a gas, can ionise the\nmolecules of this gas and unite with the neutral atoms to form\nnegative ions, while positive ions also appear. There are likewise\nproduced, at the expense of the gas still subsisting after\nrarefication within the tube, positive ions which, attracted by the\ncathode and reaching it, are not all neutralised by the negative\nelectrons, and can, if the cathode be perforated, pass through it, and\nif not, pass round it. We have then what are called the canal rays of\nGoldstein, which are deviated by an electric or magnetic field in a\ncontrary direction to the cathode rays; but, being larger, give weak\ndeviations or may even remain undeviated through losing their charge\nwhen passing through the cathode.\n\nIt may also be the parts of the walls at a distance from the cathode\nwhich send a positive rush to the latter, by a similar mechanism. It\nmay be, again, that in certain regions of the tube cathode rays are\nmet with diffused by some solid object, without having thereby changed\ntheir nature. All these complexities have been cleared up by M.\nVillard, who has published, on these questions, some remarkably\ningenious and particularly careful experiments.\n\nM. Villard has also studied the phenomena of the coiling of the rays\nin a field, as already pointed out by Hittorf and Pluecker. When a\nmagnetic field acts on the cathode particle, the latter follows a\ntrajectory, generally helicoidal, which is anticipated by the theory.\nWe here have to do with a question of ballistics, and experiments duly\nconfirm the anticipations of the calculation. Nevertheless, rather\nsingular phenomena appear in the case of certain values of the field,\nand these phenomena, dimly seen by Pluecker and Birkeland, have been\nthe object of experiments by M. Villard. The two faces of the cathode\nseem to emit rays which are deviated in a direction perpendicular to\nthe lines of force by an electric field, and do not seem to be\nelectrified. M. Villard calls them magneto-cathode rays, and according\nto M. Fortin these rays may be ordinary cathode rays, but of very\nslight velocity.\n\nIn certain cases the cathode itself may be superficially\ndisaggregated, and extremely tenuous particles detach themselves,\nwhich, being carried off at right angles to its surface, may deposit\nthemselves like a very thin film on objects placed in their path.\nVarious physicists, among them M. Houllevigue, have studied this\nphenomenon, and in the case of pressures between 1/20 and 1/100 of a\nmillimetre, the last-named scholar has obtained mirrors of most\nmetals, a phenomenon he designates by the name of ionoplasty.\n\nBut in spite of all these accessory phenomena, which even sometimes\nconceal those first observed, the existence of the electron in the\ncathodic flux remains the essential characteristic.\n\nThe electron can be apprehended in the cathodic ray by the study of\nits essential properties; and J.J. Thomson gave great value to the\nhypothesis by his measurements. At first he meant to determine the\nspeed of the cathode rays by direct experiment, and by observing, in a\nrevolving mirror, the relative displacement of two bands due to the\nexcitement of two fluorescent screens placed at different distances\nfrom the cathode. But he soon perceived that the effect of the\nfluorescence was not instantaneous, and that the lapse of time might\nform a great source of error, and he then had recourse to indirect\nmethods. It is possible, by a simple calculation, to estimate the\ndeviations produced on the rays by a magnetic and an electric field\nrespectively as a function of the speed of propagation and of the\nrelation of the charge to the material mass of the electron. The\nmeasurement of these deviations will then permit this speed and this\nrelation to be ascertained.\n\nOther processes may be used which all give the same two quantities by\ntwo suitably chosen measurements. Such are the radius of the curve\ntaken by the trajectory of the pencil in a perpendicular magnetic\nfield and the measure of the fall of potential under which the\ndischarge takes place, or the measure of the total quantity\nof electricity carried in one second and the measure of the\ncalorific energy which may be given, during the same period, to a\nthermo-electric junction. The results agree as well as can be expected,\nhaving regard to the difficulty of the experiments; the values of the\nspeed agree also with those which Professor Wiechert has obtained by\ndirect measurement.\n\nThe speed never depends on the nature of the gas contained in the\nCrookes tube, but varies with the value of the fall of potential at\nthe cathode. It is of the order of one tenth of the speed of light,\nand it may rise as high as one third. The cathode particle therefore\ngoes about three thousand times faster than the earth in its orbit.\nThe relation is also invariable, even when the substance of which the\ncathode is formed is changed or one gas is substituted for another. It\nis, on the average, a thousand times greater than the corresponding\nrelation in electrolysis. As experiment has shown, in all the\ncircumstances where it has been possible to effect measurements, the\nequality of the charges carried by all corpuscules, ions, atoms, etc.,\nwe ought to consider that the charge of the electron is here, again,\nthat of a univalent ion in electrolysis, and therefore that its mass\nis only a small fraction of that of the atom of hydrogen, viz., of the\norder of about a thousandth part. This is the same result as that to\nwhich we were led by the study of flames.\n\nThe thorough examination of the cathode radiation, then, confirms us\nin the idea that every material atom can be dissociated and will yield\nan electron much smaller than itself--and always identical whatever\nthe matter whence it comes,--the rest of the atom remaining charged\nwith a positive quantity equal and contrary to that borne by the\nelectron. In the present case these positive ions are no doubt those\nthat we again meet with in the canal rays. Professor Wien has shown\nthat their mass is really, in fact, of the order of the mass of atoms.\nAlthough they are all formed of identical electrons, there may be\nvarious cathode rays, because the velocity is not exactly the same for\nall electrons. Thus is explained the fact that we can separate them\nand that we can produce a sort of spectrum by the action of the\nmagnet, or, again, as M. Deslandres has shown in a very interesting\nexperiment, by that of an electrostatic field. This also probably\nexplains the phenomena studied by M. Villard, and previously pointed\nout.\n\n\nSec. 2. RADIOACTIVE SUBSTANCES\n\nEven in ordinary conditions, certain substances called radioactive\nemit, quite outside any particular reaction, radiations complex\nindeed, but which pass through fairly thin layers of minerals, impress\nphotographic plates, excite fluorescence, and ionize gases. In these\nradiations we again find electrons which thus escape spontaneously\nfrom radioactive bodies.\n\nIt is not necessary to give here a history of the discovery of radium,\nfor every one knows the admirable researches of M. and Madame Curie.\nBut subsequent to these first studies, a great number of facts have\naccumulated for the last six years, among which some people find\nthemselves a little lost. It may, perhaps, not be useless to indicate\nthe essential results actually obtained.\n\nThe researches on radioactive substances have their starting-point in\nthe discovery of the rays of uranium made by M. Becquerel in 1896. As\nearly as 1867 Niepce de St Victor proved that salts of uranium\nimpressed photographic plates in the dark; but at that time the\nphenomenon could only pass for a singularity attributable to\nphosphorescence, and the valuable remarks of Niepce fell into\noblivion. M. Becquerel established, after some hesitations natural in\nthe face of phenomena which seemed so contrary to accepted ideas, that\nthe radiating property was absolutely independent of phosphorescence,\nthat all the salts of uranium, even the uranous salts which are not\nphosphorescent, give similar radiant effects, and that these phenomena\ncorrespond to a continuous emission of energy, but do not seem to be\nthe result of a storage of energy under the influence of some external\nradiation. Spontaneous and constant, the radiation is insensible to\nvariations of temperature and light.\n\nThe nature of these radiations was not immediately understood,[32] and\ntheir properties seemed contradictory. This was because we were not\ndealing with a single category of rays. But amongst all the effects\nthere is one which constitutes for the radiations taken as a whole, a\nveritable process for the measurement of radioactivity. This is their\nionizing action on gases. A very complete study of the conductivity of\nair under the influence of rays of uranium has been made by various\nphysicists, particularly by Professor Rutherford, and has shown that\nthe laws of the phenomenon are the same as those of the ionization due\nto the action of the Roentgen rays.\n\n[Footnote 32: In his work on _L'Evolution de la Matiere_, M. Gustave\nLe Bon recalls that in 1897 he published several notes in the Academie\ndes Sciences, in which he asserted that the properties of uranium were\nonly a particular case of a very general law, and that the radiations\nemitted did not polarize, and were akin by their properties to the X\nrays.]\n\nIt was natural to ask one's self if the property discovered in salts\nof uranium was peculiar to this body, or if it were not, to a more or\nless degree, a general property of matter. Madame Curie and M.\nSchmidt, independently of each other, made systematic researches in\norder to solve the question; various compounds of nearly all the\nsimple bodies at present known were thus passed in review, and it was\nestablished that radioactivity was particularly perceptible in the\ncompounds of uranium and thorium, and that it was an atomic property\nlinked to the matter endowed with it, and following it in all its\ncombinations. In the course of her researches Madame Curie observed\nthat certain pitchblendes (oxide of uranium ore, containing also\nbarium, bismuth, etc.) were four times more active (activity being\nmeasured by the phenomenon of the ionization of the air) than metallic\nuranium. Now, no compound containing any other active metal than\nuranium or thorium ought to show itself more active than those metals\nthemselves, since the property belongs to their atoms. It seemed,\ntherefore, probable that there existed in pitchblendes some substance\nyet unknown, in small quantities and more radioactive than uranium.\n\nM. and Madame Curie then commenced those celebrated experiments which\nbrought them to the discovery of radium. Their method of research has\nbeen justly compared in originality and importance to the process of\nspectrum analysis. To isolate a radioactive substance, the first thing\nis to measure the activity of a certain compound suspected of\ncontaining this substance, and this compound is chemically separated.\nWe then again take in hand all the products obtained, and by measuring\ntheir activity anew, it is ascertained whether the substance sought\nfor has remained in one of these products, or is divided among them,\nand if so, in what proportion. The spectroscopic reaction which we may\nuse in the course of this separation is a thousand times less\nsensitive than observation of the activity by means of the\nelectrometer.\n\nThough the principle on which the operation of the concentration of\nthe radium rests is admirable in its simplicity, its application is\nnevertheless very laborious. Tons of uranium residues have to be\ntreated in order to obtain a few decigrammes of pure salts of radium.\nRadium is characterised by a special spectrum, and its atomic weight,\nas determined by Madame Curie, is 225; it is consequently the higher\nhomologue of barium in one of the groups of Mendeleef. Salts of radium\nhave in general the same chemical properties as the corresponding\nsalts of barium, but are distinguished from them by the differences of\nsolubility which allow of their separation, and by their enormous\nactivity, which is about a hundred thousand times greater than that of\nuranium.\n\nRadium produces various chemical and some very intense physiological\nreactions. Its salts are luminous in the dark, but this luminosity, at\nfirst very bright, gradually diminishes as the salts get older. We\nhave here to do with a secondary reaction correlative to the\nproduction of the emanation, after which radium undergoes the\ntransformations which will be studied later on.\n\nThe method of analysis founded by M. and Madame Curie has enabled\nother bodies presenting sensible radioactivity to be discovered. The\nalkaline metals appear to possess this property in a slight degree.\nRecently fallen snow and mineral waters manifest marked action. The\nphenomenon may often be due, however, to a radioactivity induced by\nradiations already existing in the atmosphere. But this radioactivity\nhardly attains the ten-thousandth part of that presented by uranium,\nor the ten-millionth of that appertaining to radium.\n\nTwo other bodies, polonium and actinium, the one characterised by the\nspecial nature of the radiations it emits and the other by a\nparticular spectrum, seem likewise to exist in pitchblende. These\nchemical properties have not yet been perfectly defined; thus M.\nDebierne, who discovered actinium, has been able to note the active\nproperty which seems to belong to it, sometimes in lanthanum,\nsometimes in neodynium.[33] It is proved that all extremely\nradioactive bodies are the seat of incessant transformations, and even\nnow we cannot state the conditions under which they present themselves\nin a strictly determined form.\n\n[Footnote 33: Polonium has now been shown to be no new element, but\none of the transformation products of radium. Radium itself is also\nthought to be derived in some manner, not yet ascertained, from\nuranium. The same is the case with actinium, which is said to come in\nthe long run from uranium, but not so directly as does radium. All\nthis is described in Professor Rutherford's _Radioactive\nTransformations_ (London, 1906).--ED.]\n\n\nSec. 3. THE RADIATION OF THE RADIOACTIVE BODIES AND THE EMANATION\n\nTo acquire exact notions as to the nature of the rays emitted by the\nradioactive bodies, it was necessary to try to cause magnetic or\nelectric forces to act on them so as to see whether they behaved in\nthe same way as light and the X rays, or whether like the cathode rays\nthey were deviated by a magnetic field. This work was effected by\nProfessor Giesel, then by M. Becquerel, Professor Rutherford, and by\nmany other experimenters after them. All the methods which have\nalready been mentioned in principle have been employed in order to\ndiscover whether they were electrified, and, if so, by electricity of\nwhat sign, to measure their speed, and to ascertain their degree of\npenetration.\n\nThe general result has been to distinguish three sorts of radiations,\ndesignated by the letters alpha, beta, gamma.\n\nThe alpha rays are positively charged, and are projected at a speed\nwhich may attain the tenth of that of light; M.H. Becquerel has shown\nby the aid of photography that they are deviated by a magnet, and\nProfessor Rutherford has, on his side, studied this deviation by the\nelectrical method. The relation of the charge to the mass is, in the\ncase of these rays, of the same order as in that of the ions of\nelectrolysis. They may therefore be considered as exactly analogous to\nthe canal rays of Goldstein, and we may attribute them to a material\ntransport of corpuscles of the magnitude of atoms. The relatively\nconsiderable size of these corpuscles renders them very absorbable. A\nflight of a few millimetres in a gas suffices to reduce their number\nby one-half. They have great ionizing power.\n\nThe beta rays are on all points similar to the cathode rays; they are,\nas M. and Madame Curie have shown, negatively charged, and the charge\nthey carry is always the same. Their size is that of the electrons,\nand their velocity is generally greater than that of the cathode rays,\nwhile it may become almost that of light. They have about a hundred\ntimes less ionizing power than the alpha rays.\n\nThe gamma rays were discovered by M. Villard.[34] They may be compared\nto the X rays; like the latter, they are not deviated by the magnetic\nfield, and are also extremely penetrating. A strip of aluminium five\nmillimetres thick will stop the other kinds, but will allow them to\npass. On the other hand, their ionizing power is 10,000 times less\nthan that of the alpha rays.\n\n[Footnote 34: This is admitted by Professor Rutherford (_Radio-Activity_,\nCamb., 1904, p. 141) and Professor Soddy (_Radio-Activity_, London,\n1904, p. 66). Neither Mr Whetham, in his Recent _Development of\nPhysical Science_ (London, 1904) nor the Hon. R.J. Strutt in _The\nBecquerel Rays_ (London, same date), both of whom deal with the\nhistorical side of the subject, seem to have noticed the fact.--ED.]\n\nTo these radiations there sometimes are added in the course of\nexperiments secondary radiations analogous to those of M. Sagnac, and\nproduced when the alpha, beta, or gamma rays meet various substances.\nThis complication has often led to some errors of observation.\n\nPhosphorescence and fluorescence seem especially to result from the\nalpha and beta rays, particularly from the alpha rays, to which\nbelongs the most important part of the total energy of the radiation.\nSir W. Crookes has invented a curious little apparatus, the\nspinthariscope, which enables us to examine the phosphorescence of the\nblende excited by these rays. By means of a magnifying glass, a screen\ncovered with sulphide of zinc is kept under observation, and in front\nof it is disposed, at a distance of about half a millimetre, a\nfragment of some salt of radium. We then perceive multitudes of\nbrilliant points on the screen, which appear and at once disappear,\nproducing a scintillating effect. It seems probable that every\nparticle falling on the screen produces by its impact a disturbance in\nthe neighbouring region, and it is this disturbance which the eye\nperceives as a luminous point. Thus, says Sir W. Crookes, each drop of\nrain falling on the surface of still water is not perceived as a drop\nof rain, but by reason of the slight splash which it causes at the\nmoment of impact, and which is manifested by ridges and waves\nspreading themselves in circles.\n\nThe various radioactive substances do not all give radiations of\nidentical constitution. Radium and thorium possess in somewhat large\nproportions the three kinds of rays, and it is the same with actinium.\nPolonium contains especially alpha rays and a few gamma rays.[35] In\nthe case of uranium, the alpha rays have extremely slight penetrating\npower, and cannot even impress photographic plates. But the widest\ndifference between the substances proceeds from the emanation. Radium,\nin addition to the three groups of rays alpha, beta, and gamma,\ndisengages continuously an extremely subtle emanation, seemingly\nalmost imponderable, but which may be, for many reasons, looked upon\nas a vapour of which the elastic force is extremely feeble.\n\n[Footnote 35: It has now been shown that polonium when freshly\nseparated emits beta rays also; see Dr Logeman's paper in _Proceedings\nof the Royal Society_, A., 6th September 1906.--ED.]\n\nM. and Madame Curie discovered as early as 1899 that every substance\nplaced in the neighbourhood of radium, itself acquired a radioactivity\nwhich persisted for several hours after the removal of the radium.\nThis induced radioactivity seems to be carried to other bodies by the\nintermediary of a gas. It goes round obstacles, but there must exist\nbetween the radium and the substance a free and continuous space for\nthe activation to take place; it cannot, for instance, do so through a\nwall of glass.\n\nIn the case of compounds of thorium Professor Rutherford discovered a\nsimilar phenomenon; since then, various physicists, Professor Soddy,\nMiss Brooks, Miss Gates, M. Danne, and others, have studied the\nproperties of these emanations.\n\nThe substance emanated can neither be weighed nor can its elastic\nforce be ascertained; but its transformations may be followed, as it\nis luminous, and it is even more certainly characterised by its\nessential property, i.e. its radioactivity. We also see that it can be\ndecanted like a gas, that it will divide itself between two tubes of\ndifferent capacity in obedience to the law of Mariotte, and will\ncondense in a refrigerated tube in accordance with the principle of\nWatt, while it even complies with the law of Gay-Lussac.\n\nThe activity of the emanation vanishes quickly, and at the end of four\ndays it has diminished by one-half. If a salt of radium is heated, the\nemanation becomes more abundant, and the residue, which, however, does\nnot sensibly diminish in weight, will have lost all its radioactivity,\nand will only recover it by degrees. Professor Rutherford,\nnotwithstanding many different attempts, has been unable to make this\nemanation enter into any chemical reaction. If it be a gaseous body,\nit must form part of the argon group, and, like its other members, be\nperfectly inert.\n\nBy studying the spectrum of the gas disengaged by a solution of salt\nof radium, Sir William Ramsay and Professor Soddy remarked that when\nthe gas is radioactive there are first obtained rays of gases\nbelonging to the argon family, then by degrees, as the activity\ndisappears, the spectrum slowly changes, and finally presents the\ncharacteristic aspect of helium.\n\nWe know that the existence of this gas was first discovered by\nspectrum analysis in the sun. Later its presence was noted in our\natmosphere, and in a few minerals which happen to be the very ones\nfrom which radium has been obtained. It might therefore have been the\ncase that it pre-existed in the gases extracted from radium; but a\nremarkable experiment by M. Curie and Sir James Dewar seems to show\nconvincingly that this cannot be so. The spectrum of helium never\nappears at first in the gas proceeding from pure bromide of radium;\nbut it shows itself, on the other hand, very distinctly, after the\nradioactive transformations undergone by the salt.\n\nAll these strange phenomena suggest bold hypotheses, but to construct\nthem with any solidity they must be supported by the greatest possible\nnumber of facts. Before admitting a definite explanation of the\nphenomena which have their seat in the curious substances discovered\nby them, M. and Madame Curie considered, with a great deal of reason,\nthat they ought first to enrich our knowledge with the exact and\nprecise facts relating to these bodies and to the effects produced by\nthe radiations they emit.\n\nThus M. Curie particularly set himself to study the manner in which\nthe radioactivity of the emanation is dissipated, and the\nradioactivity that this emanation can induce on all bodies. The\nradioactivity of the emanation diminishes in accordance with an\nexponential law. The constant of time which characterises this\ndecrease is easily and exactly determined, and has a fixed value,\nindependent of the conditions of the experiment as well as of the\nnature of the gas which is in contact with the radium and becomes\ncharged with the emanation. The regularity of the phenomenon is so\ngreat that it can be used to measure time: in 3985 seconds[36] the\nactivity is always reduced one-half.\n\n[Footnote 36: According to Professor Rutherford, in 3.77 days.--ED]\n\nRadioactivity induced on any body which has been for a long time in\npresence of a salt of radium disappears more rapidly. The phenomenon\nappears, moreover, more complex, and the formula which expresses the\nmanner in which the activity diminishes must contain two exponentials.\nTo find it theoretically we have to imagine that the emanation first\ndeposits on the body in question a substance which is destroyed in\ngiving birth to a second, this latter disappearing in its turn by\ngenerating a third. The initial and final substances would be\nradioactive, but the intermediary one, not. If, moreover, the bodies\nacted on are brought to a temperature of over 700 deg., they appear to\nlose by volatilisation certain substances condensed in them, and at\nthe same time their activity disappears.\n\nThe other radioactive bodies behave in a similar way. Bodies which\ncontain actinium are particularly rich in emanations. Uranium, on the\ncontrary, has none.[37] This body, nevertheless, is the seat of\ntransformations comparable to those which the study of emanations\nreveals in radium; Sir W. Crookes has separated from uranium a matter\nwhich is now called uranium X. This matter is at first much more\nactive than its parent, but its activity diminishes rapidly, while the\nordinary uranium, which at the time of the separation loses its\nactivity, regains it by degrees. In the same way, Professors\nRutherford and Soddy have discovered a so-called thorium X to be the\nstage through which ordinary thorium has to pass in order to produce\nits emanation.[38]\n\n[Footnote 37: Professor Rutherford has lately stated that uranium may\npossibly produce an emanation, but that its rate of decay must be too\nswift for its presence to be verified (see _Radioactive\nTransformations_, p. 161).--ED.]\n\n[Footnote 38: An actinium X was also discovered by Professor Giesel\n(_Jahrbuch d. Radioaktivitat_, i. p. 358, 1904). Since the above was\nwritten, another product has been found to intervene between the X\nsubstance and the emanation in the case of actinium and thorium. They\nhave been named radio-actinium and radio-thorium respectively.--ED.]\n\nIt is not possible to give a complete table which should, as it were,\nrepresent the genealogical tree of the various radioactive substances.\nSeveral authors have endeavoured to do so, but in a premature manner;\nall the affiliations are not at the present time yet perfectly known,\nand it will no doubt be acknowledged some day that identical states\nhave been described under different names.[39]\n\n[Footnote 39: Such a table is given on p. 169 of Rutherford's\n_Radioactive Transformations_.--ED.]\n\n\nSec. 4. THE DISAGGREGATION OF MATTER AND ATOMIC ENERGY\n\nIn spite of uncertainties which are not yet entirely removed, it\ncannot be denied that many experiments render it probable that in\nradioactive bodies we find ourselves witnessing veritable\ntransformations of matter.\n\nProfessor Rutherford, Professor Soddy, and several other physicists,\nhave come to regard these phenomena in the following way. A\nradioactive body is composed of atoms which have little stability, and\nare able to detach themselves spontaneously from the parent substance,\nand at the same time to divide themselves into two essential component\nparts, the negative electron and its residue the positive ion. The\nfirst-named constitutes the beta, and the second the alpha rays.\n\nThe emanation is certainly composed of alpha ions with a few molecules\nagglomerated round them. Professor Rutherford has, in fact,\ndemonstrated that the emanation is charged with positive electricity;\nand this emanation may, in turn, be destroyed by giving birth to new\nbodies.\n\nAfter the loss of the atoms which are carried off by the radiation,\nthe remainder of the body acquires new properties, but it may still be\nradioactive, and again lose atoms. The various stages that we meet\nwith in the evolution of the radioactive substance or of its\nemanation, correspond to the various degrees of atomic disaggregation.\nProfessors Rutherford and Soddy have described them clearly in the\ncase of uranium and radium. As regards thorium the results are less\nsatisfactory. The evolution should continue until a stable atomic\ncondition is finally reached, which, because of this stability, is no\nlonger radioactive. Thus, for instance, radium would finally be\ntransformed into helium.[40]\n\n[Footnote 40: This opinion, no doubt formed when Sir William Ramsay's\ndiscovery of the formation of helium from the radium emanation was\nfirst made known, is now less tenable. The latest theory is that the\nalpha particle is in fact an atom of helium, and that the final\ntransformation product of radium and the other radioactive substances\nis lead. Cf. Rutherford, op. cit. passim.--ED.]\n\nIt is possible, by considerations analogous to those set forth above\nin other cases, to arrive at an idea of the total number of particles\nper second expelled by one gramme of radium; Professor Rutherford in\nhis most recent evaluation finds that this number approaches 2.5 x\n10^{11}.[41] By calculating from the atomic weight the number of atoms\nprobably contained in this gramme of radium, and supposing each\nparticle liberated to correspond to the destruction of one atom, it is\nfound that one half of the radium should disappear in 1280 years;[42]\nand from this we may conceive that it has not yet been possible to\ndiscover any sensible loss of weight. Sir W. Ramsay and Professor\nSoddy attained a like result by endeavouring to estimate the mass of\nthe emanation by the quantity of helium produced.\n\n[Footnote 41: See _Radioactive Transformations_ (p. 251). Professor\nRutherford says that \"each of the alpha ray products present in one\ngram of radium product (_sic_) expels 6.2 x 10^{10} alpha particles\nper second.\" He also remarks on \"the experimental difficulty of\naccurately determining the number of alpha particles expelled from\nradium per second.\"--ED.]\n\n[Footnote 42: See Rutherford, op. cit. p. 150.--ED.]\n\nIf radium transforms itself in such a way that its activity does not\npersist throughout the ages, it loses little by little the provision\nof energy it had in the beginning, and its properties furnish no valid\nargument to oppose to the principle of the conservation of energy. To\nput everything right, we have only to recognise that radium possessed\nin the potential state at its formation a finite quantity of energy\nwhich is consumed little by little. In the same manner, a chemical\nsystem composed, for instance, of zinc and sulphuric acid, also\ncontains in the potential state energy which, if we retard the\nreaction by any suitable arrangement--such as by amalgamating the zinc\nand by constituting with its elements a battery which we cause to act\non a resistance--may be made to exhaust itself as slowly as one may\ndesire.\n\nThere can, therefore, be nothing in any way surprising in the fact\nthat a combination which, like the atomic combination of radium, is\nnot stable--since it disaggregates itself,--is capable of\nspontaneously liberating energy, but what may be a little astonishing,\nat first sight, is the considerable amount of this energy.\n\nM. Curie has calculated directly, by the aid of the calorimeter, the\nquantity of energy liberated, measuring it entirely in the form of\nheat. The disengagement of heat accounted for in a grain of radium is\nuniform, and amounts to 100 calories per hour. It must therefore be\nadmitted that an atom of radium, in disaggregating itself, liberates\n30,000 times more energy than a molecule of hydrogen when the latter\ncombines with an atom of oxygen to form a molecule of water.\n\nWe may ask ourselves how the atomic edifice of the active body can be\nconstructed, to contain so great a provision of energy. We will remark\nthat such a question might be asked concerning cases known from the\nmost remote antiquity, like that of the chemical systems, without any\nsatisfactory answer ever being given. This failure surprises no one,\nfor we get used to everything--even to defeat.\n\nWhen we come to deal with a new problem we have really no right to\nshow ourselves more exacting; yet there are found persons who refuse\nto admit the hypothesis of the atomic disaggregation of radium because\nthey cannot have set before them a detailed plan of that complex whole\nknown to us as an atom.\n\nThe most natural idea is perhaps the one suggested by comparison with\nthose astronomical phenomena where our observation most readily allows\nus to comprehend the laws of motion. It corresponds likewise to the\ntendency ever present in the mind of man, to compare the infinitely\nsmall with the infinitely great. The atom may be regarded as a sort of\nsolar system in which electrons in considerable numbers gravitate\nround the sun formed by the positive ion. It may happen that certain\nof these electrons are no longer retained in their orbit by the\nelectric attraction of the rest of the atom, and may be projected from\nit like a small planet or comet which escapes towards the stellar\nspaces. The phenomena of the emission of light compels us to think\nthat the corpuscles revolve round the nucleus with extreme velocities,\nor at the rate of thousands of billions of evolutions per second. It\nis easy to conceive from this that, notwithstanding its lightness, an\natom thus constituted may possess an enormous energy.[43]\n\n[Footnote 43: This view of the case has been made very clear by M.\nGustave le Bon in _L'Evolution de la Matiere_ (Paris, 1906). See\nespecially pp. 36-52, where the amount of the supposed intra-atomic\nenergy is calculated.--ED.]\n\nOther authors imagine that the energy of the corpuscles is principally\ndue to the extremely rapid rotations of those elements on their own\naxes. Lord Kelvin lately drew up on another model the plan of a\nradioactive atom capable of ejecting an electron with a considerable\n_vis viva_. He supposes a spherical atom formed of concentric layers\nof positive and negative electricity disposed in such a way that its\nexternal action is null, and that, nevertheless, the force emanated\nfrom the centre may be repellent for certain values when the electron\nis within it.\n\nThe most prudent physicists and those most respectful to established\nprinciples may, without any scruples, admit the explanation of the\nradioactivity of radium by a dislocation of its molecular edifice. The\nmatter of which it is constituted evolves from an admittedly unstable\ninitial state to another stable one. It is, in a way, a slow\nallotropic transformation which takes place by means of a mechanism\nregarding which, in short, we have no more information than we have\nregarding other analogous transformations. The only astonishment we\ncan legitimately feel is derived from the thought that we are suddenly\nand deeply penetrating to the very heart of things.\n\nBut those persons who have a little more hardihood do not easily\nresist the temptation of forming daring generalisations. Thus it will\noccur to some that this property, already discovered in many\nsubstances where it exists in more or less striking degree, is, with\ndifferences of intensity, common to all bodies, and that we are thus\nconfronted by a phenomenon derived from an essential quality of\nmatter. Quite recently, Professor Rutherford has demonstrated in a\nfine series of experiments that the alpha particles of radium cease to\nionize gases when they are made to lose their velocity, but that they\ndo not on that account cease to exist. It may follow that many bodies\nemit similar particles without being easily perceived to do so; since\nthe electric action, by which this phenomenon of radioactivity is\ngenerally manifested, would, in this case, be but very weak.\n\nIf we thus believe radioactivity to be an absolutely general\nphenomenon, we find ourselves face to face with a new problem. The\ntransformation of radioactive bodies can no longer be assimilated to\nallotropic transformations, since thus no final form could ever be\nattained, and the disaggregation would continue indefinitely up to the\ncomplete dislocation of the atom.[44] The phenomenon might, it is\ntrue, have a duration of perhaps thousands of millions of centuries,\nbut this duration is but a minute in the infinity of time, and matters\nlittle. Our habits of mind, if we adopt such a conception, will be\nnone the less very deeply disturbed. We shall have to abandon the idea\nso instinctively dear to us that matter is the most stable thing in\nthe universe, and to admit, on the contrary, that all bodies whatever\nare a kind of explosive decomposing with extreme slowness. There is in\nthis, whatever may have been said, nothing contrary to any of the\nprinciples on which the science of energetics rests; but an hypothesis\nof this nature carries with it consequences which ought in the highest\ndegree to interest the philosopher, and we all know with what alluring\nboldness M. Gustave Le Bon has developed all these consequences in his\nwork on the evolution of matter.[45]\n\n[Footnote 44: This is the main contention of M. Gustave Le Bon in\nhis work last quoted.--ED.]\n\n[Footnote 45: See last note.--ED.]\n\nThere is hardly a physicist who does not at the present day adopt in\none shape or another the ballistic hypothesis. All new facts are\nco-ordinated so happily by it, that it more and more satisfies our\nminds; but it cannot be asserted that it forces itself on our\nconvictions with irresistible weight. Another point of view appeared\nmore plausible and simple at the outset, when there seemed reason to\nconsider the energy radiated by radioactive bodies as inexhaustible.\nIt was thought that the source of this energy was to be looked for\nwithout the atom, and this idea may perfectly well he maintained at\nthe present day.\n\nRadium on this hypothesis must be considered as a transformer\nborrowing energy from the external medium and returning it in the form\nof radiation. It is not impossible, even, to admit that the energy\nwhich the atom of radium withdraws from the surrounding medium may\nserve to keep up, not only the heat emitted and its complex radiation,\nbut also the dissociation, supposed to be endothermic, of this atom.\nSuch seems to be the idea of M. Debierne and also of M. Sagnac. It\ndoes not seem to accord with the experiments that this borrowed energy\ncan be a part of the heat of the ambient medium; and, indeed, such a\nphenomenon would be contrary to the principle of Carnot if we wished\n(though we have seen how disputable is this extension) to extend this\nprinciple to the phenomena which are produced in the very bosom of the\natom.\n\nWe may also address ourselves to a more noble form of energy, and ask\nourselves whether we are not, for the first time, in presence of a\ntransformation of gravitational energy. It may be singular, but it is\nnot absurd, to suppose that the unit of mass of radium is not attached\nto the earth with the same intensity as an inert body. M. Sagnac has\ncommenced some experiments, as yet unpublished, in order to study the\nlaws of the fall of a fragment of radium. They are necessarily very\ndelicate, and the energetic and ingenious physicist has not yet\nsucceeded in finishing them.[46] Let us suppose that he succeeds in\ndemonstrating that the intensity of gravity is less for radium than\nfor the platinum or the copper of which the pendulums used to\nillustrate the law of Newton are generally made; it would then be\npossible still to think that the laws of universal attraction are\nperfectly exact as regards the stars, and that ponderability is really\na particular case of universal attraction, while in the case of\nradioactive bodies part of the gravitational energy is transformed in\nthe course of its evolution and appears in the form of active\nradiation.\n\n[Footnote 46: In reality M. Sagnac operated in the converse manner. He\ntook two equal _weights_ of a salt of radium and a salt of barium,\nwhich he made oscillate one after the other in a torsion balance. Had\nthe durations of oscillation been different, it might be concluded\nthat the mechanical mass is not the same for radium as for barium.]\n\nBut for this explanation to be admitted, it would evidently need to be\nsupported by very numerous facts. It might, no doubt, appear still\nmore probable that the energy borrowed from the external medium by\nradium is one of those still unknown to us, but of which a vague\ninstinct causes us to suspect the existence around us. It is\nindisputable, moreover, that the atmosphere in all directions is\nfurrowed with active radiations; those of radium may be secondary\nradiations reflected by a kind of resonance phenomenon.\n\nCertain experiments by Professors Elster and Geitel, however, are not\nfavourable to this point of view. If an active body be surrounded by a\nradioactive envelope, a screen should prevent this body from receiving\nany impression from outside, and yet there is no diminution apparent\nin the activity presented by a certain quantity of radium when it is\nlowered to a depth of 800 metres under ground, in a region containing\na notable quantity of pitchblende. These negative results are, on the\nother hand, so many successes for the partisans of the explanation of\nradioactivity by atomic energy.\n\n\n\n\nCHAPTER X\n\nTHE ETHER AND MATTER\n\n\nSec. 1. THE RELATIONS BETWEEN THE ETHER AND MATTER\n\nFor some time past it has been the more or less avowed ambition of\nphysicists to construct with the particles of ether all possible forms\nof corporeal existence; but our knowledge of the inmost nature of\nthings has hitherto seemed too limited for us to attempt such an\nenterprise with any chance of success. The electronic hypothesis,\nhowever, which has furnished a satisfactory image of the most curious\nphenomena produced in the bosom of matter, has also led to a more\ncomplete electromagnetic theory of the ether than that of Maxwell, and\nthis twofold result has given birth to the hope of arriving by means\nof this hypothesis at a complete co-ordination of the physical world.\n\nThe phenomena whose study may bring us to the very threshold of the\nproblem, are those in which the connections between matter and the\nether appear clearly and in a relatively simple manner. Thus in the\nphenomena of emission, ponderable matter is seen to give birth to\nwaves which are transmitted by the ether, and by the phenomena of\nabsorption it is proved that these waves disappear and excite\nmodifications in the interior of the material bodies which receive\nthem. We here catch in operation actual reciprocal actions and\nreactions between the ether and matter. If we could thoroughly\ncomprehend these actions, we should no doubt be in a position to fill\nup the gap which separates the two regions separately conquered by\nphysical science.\n\nIn recent years numerous researches have supplied valuable materials\nwhich ought to be utilized by those endeavouring to construct a theory\nof radiation. We are, perhaps, still ill informed as to the phenomena\nof luminescence in which undulations are produced in a complex manner,\nas in the case of a stick of moist phosphorus which is luminescent in\nthe dark, or in that of a fluorescent screen. But we are very well\nacquainted with emission or absorption by incandescence, where the\nonly transformation is that of calorific into radiating energy, or\n_vice versa_. It is in this case alone that can be correctly applied\nthe celebrated demonstration by which Kirchhoff established, by\nconsiderations borrowed from thermodynamics, the proportional\nrelations between the power of emission and that of absorption.\n\nIn treating of the measurement of temperature, I have already pointed\nout the experiments of Professors Lummer and Pringsheim and the\ntheoretical researches of Stephan and Professor Wien. We may consider\nthat at the present day the laws of the radiation of dark bodies are\ntolerably well known, and, in particular, the manner in which each\nelementary radiation increases with the temperature. A few doubts,\nhowever, subsist with respect to the law of the distribution of energy\nin the spectrum. In the case of real and solid bodies the results are\nnaturally less simple than in that of dark bodies. One side of the\nquestion has been specially studied on account of its great practical\ninterest, that is to say, the fact that the relation of the luminous\nenergy to the total amount radiated by a body varies with the nature\nof this last; and the knowledge of the conditions under which this\nrelation becomes most considerable led to the discovery of\nincandescent lighting by gas in the Auer-Welsbach mantle, and to the\nsubstitution for the carbon thread in the electric light bulb of a\nfilament of osmium or a small rod of magnesium, as in the Nernst lamp.\nCareful measurements effected by M. Fery have furnished, in\nparticular, important information on the radiation of the white\noxides; but the phenomena noticed have not yet found a satisfactory\ninterpretation. Moreover, the radiation of calorific origin is here\naccompanied by a more or less important luminescence, and the problem\nbecomes very complex.\n\nIn the same way that, for the purpose of knowing the constitution of\nmatter, it first occurred to us to investigate gases, which appear to\nbe molecular edifices built on a more simple and uniform plan than\nsolids, we ought naturally to think that an examination of the\nconditions in which emission and absorption are produced by gaseous\nbodies might be eminently profitable, and might perhaps reveal the\nmechanism by which the relations between the molecule of the ether and\nthe molecule of matter might be established.\n\nUnfortunately, if a gas is not absolutely incapable of emitting some\nsort of rays by simple heat, the radiation thus produced, no doubt by\nreason of the slightness of the mass in play, always remains of\nmoderate intensity. In nearly all the experiments, new energies of\nchemical or electrical origin come into force. On incandescence,\nluminescence is superposed; and the advantage which might have been\nexpected from the simplicity of the medium vanishes through the\ncomplication of the circumstances in which the phenomenon is produced.\n\nProfessor Pringsheim has succeeded, in certain cases, in finding the\ndividing line between the phenomena of luminescence and that of\nincandescence. Thus the former takes a predominating importance when\nthe gas is rendered luminous by electrical discharges, and chemical\ntransformations, especially, play a preponderant role in the emission\nof the spectrum of flames which contain a saline vapour. In all the\nordinary experiments of spectrum analysis the laws of Kirchhoff cannot\ntherefore be considered as established, and yet the relation between\nemission and absorption is generally tolerably well verified. No doubt\nwe are here in presence of a kind of resonance phenomenon, the gaseous\natoms entering into vibration when solicited by the ether by a motion\nidentical with the one they are capable of communicating to it.\n\nIf we are not yet very far advanced in the study of the mechanism of\nthe production of the spectrum,[47] we are, on the other hand, well\nacquainted with its constitution. The extreme confusion which the\nspectra of the lines of the gases seemed to present is now, in great\npart at least, cleared up. Balmer gave some time since, in the case of\nthe hydrogen spectrum, an empirical formula which enabled the rays\ndiscovered later by an eminent astronomer, M. Deslandres, to be\nrepresented; but since then, both in the cases of line and band\nspectra, the labours of Professor Rydberg, of M. Deslandres, of\nProfessors Kayzer and Runge, and of M. Thiele, have enabled us to\ncomprehend, in their smallest details, the laws of the distribution of\nlines and bands.\n\n[Footnote 47: Many theories as to the cause of the lines and bands of\nthe spectrum have been put forward since this was written, among which\nthat of Professor Stark (for which see _Physikalische Zeitschrift_ for\n1906, passim) is perhaps the most advanced. That of M. Jean Becquerel,\nwhich would attribute it to the vibration within the atom of both\nnegative and positive electrons, also deserves notice. A popular\naccount of this is given in the _Athenaeum_ of 20th April 1907.--ED.]\n\nThese laws are simple, but somewhat singular. The radiations emitted\nby a gas cannot be compared to the notes to which a sonorous body\ngives birth, nor even to the most complicated vibrations of any\nelastic body. The number of vibrations of the different rays are not\nthe successive multiples of one and the same number, and it is not a\nquestion of a fundamental radiation and its harmonics, while--and this\nis an essential difference--the number of vibrations of the radiation\ntend towards a limit when the period diminishes infinitely instead of\nconstantly increasing, as would be the case with the vibrations of\nsound.\n\nThus the assimilation of the luminous to the elastic vibration is not\ncorrect. Once again we find that the ether does not behave like matter\nwhich obeys the ordinary laws of mechanics, and every theory must take\nfull account of these curious peculiarities which experiment reveals.\n\nAnother difference, likewise very important, between the luminous and\nthe sonorous vibrations, which also points out how little analogous\ncan be the constitutions of the media which transmit the vibrations,\nappears in the phenomena of dispersion. The speed of propagation,\nwhich, as we have seen when discussing the measurement of the velocity\nof sound, depends very little on the musical note, is not at all the\nsame in the case of the various radiations which can be propagated in\nthe same substance. The index of refraction varies with the duration\nof the period, or, if you will, with the length of wave _in vacuo_\nwhich is proportioned to this duration, since _in vacuo_ the speed of\npropagation is entirely the same for all vibrations.\n\nCauchy was the first to propose a theory on which other attempts have\nbeen modelled; for example, the very interesting and simple one of\nBriot. This last-named supposed that the luminous vibration could not\nperceptibly drag with it the molecular material of the medium across\nwhich it is propagated, but that matter, nevertheless, reacts on the\nether with an intensity proportional to the elongation, in such a\nmanner as tends to bring it back to its position of equilibrium. With\nthis simple hypothesis we can fairly well interpret the phenomena of\nthe dispersion of light in the case of transparent substances; but far\nfrom well, as M. Carvallo has noted in some extremely careful\nexperiments, the dispersion of the infra-red spectrum, and not at all\nthe peculiarities presented by absorbent substances.\n\nM. Boussinesq arrives at almost similar results, by attributing\ndispersion, on the other hand, to the partial dragging along of\nponderable matter and to its action on the ether. By combining, in a\nmeasure, as was subsequently done by M. Boussinesq, the two\nhypotheses, formulas can be established far better in accord with all\nthe known facts.\n\nThese facts are somewhat complex. It was at first thought that the\nindex always varied in inverse ratio to the wave-length, but numerous\nsubstances have been discovered which present the phenomenon of\nabnormal dispersion--that is to say, substances in which certain\nradiations are propagated, on the contrary, the more quickly the\nshorter their period. This is the case with gases themselves, as\ndemonstrated, for example, by a very elegant experiment of M.\nBecquerel on the dispersion of the vapour of sodium. Moreover, it may\nhappen that yet more complications may be met with, as no substance is\ntransparent for the whole extent of the spectrum. In the case of\ncertain radiations the speed of propagation becomes nil, and the index\nshows sometimes a maximum and sometimes a minimum. All those phenomena\nare in close relation with those of absorption.\n\nIt is, perhaps, the formula proposed by Helmholtz which best accounts\nfor all these peculiarities. Helmholtz came to establish this formula\nby supposing that there is a kind of friction between the ether and\nmatter, which, like that exercised on a pendulum, here produces a\ndouble effect, changing, on the one hand, the duration of this\noscillation, and, on the other, gradually damping it. He further\nsupposed that ponderable matter is acted on by elastic forces. The\ntheory of Helmholtz has the great advantage of representing, not only\nthe phenomena of dispersion, but also, as M. Carvallo has pointed out,\nthe laws of rotatory polarization, its dispersion and other phenomena,\namong them the dichroism of the rotatory media discovered by M.\nCotton.\n\nIn the establishment of these theories, the language of ordinary\noptics has always been employed. The phenomena are looked upon as due\nto mechanical deformations or to movements governed by certain forces.\nThe electromagnetic theory leads, as we have seen, to the employment\nof other images. M.H. Poincare, and, after him, Helmholtz, have both\nproposed electromagnetic theories of dispersion. On examining things\nclosely, it will be found that there are not, in truth, in the two\nways of regarding the problem, two equivalent translations of exterior\nreality. The electrical theory gives us to understand, much better\nthan the mechanical one, that _in vacuo_ the dispersion ought to be\nstrictly null, and this absence of dispersion appears to be confirmed\nwith extraordinary precision by astronomical observations. Thus the\nobservation, often repeated, and at different times of year, proves\nthat in the case of the star Algol, the light of which takes at least\nfour years to reach us, no sensible difference in coloration\naccompanies the changes in brilliancy.\n\n\nSec. 2. THE THEORY OF LORENTZ\n\nPurely mechanical considerations have therefore failed to give an\nentirely satisfactory interpretation of the phenomena in which even\nthe simplest relations between matter and the ether appear. They\nwould, evidently, be still more insufficient if used to explain\ncertain effects produced on matter by light, which could not, without\ngrave difficulties, be attributed to movement; for instance, the\nphenomena of electrification under the influence of certain\nradiations, or, again, chemical reactions such as photographic\nimpressions.\n\nThe problem had to be approached by another road. The electromagnetic\ntheory was a step in advance, but it comes to a standstill, so to\nspeak, at the moment when the ether penetrates into matter. If we wish\nto go deeper into the inwardness of the phenomena, we must follow, for\nexample, Professor Lorentz or Dr Larmor, and look with them for a mode\nof representation which appears, besides, to be a natural consequence\nof the fundamental ideas forming the basis of Hertz's experiments.\n\nThe moment we look upon a wave in the ether as an electromagnetic\nwave, a molecule which emits light ought to be considered as a kind of\nexcitant. We are thus led to suppose that in each radiating molecule\nthere are one or several electrified particles, animated with a\nto-and-fro movement round their positions of equilibrium, and these\nparticles are certainly identical with those electrons the existence\nof which we have already admitted for so many other reasons.\n\nIn the simplest theory, we will imagine an electron which may be\ndisplaced from its position of equilibrium in all directions, and is,\nin this displacement, submitted to attractions which communicate to it\na vibration like a pendulum. These movements are equivalent to tiny\ncurrents, and the mobile electron, when animated with a considerable\nvelocity, must be sensitive to the action of the magnet which modifies\nthe form of the trajectory and the value of the period. This almost\ndirect consequence was perceived by Lorentz, and it led him to the new\nidea that radiations emitted by a body ought to be modified by the\naction of a strong electromagnet.\n\nAn experiment enabled this prevision to be verified. It was made, as\nis well known, as early as 1896 by Zeeman; and the discovery produced\na legitimate sensation. When a flame is subjected to the action of a\nmagnetic field, a brilliant line is decomposed in conditions more or\nless complex which an attentive study, however, allows us to define.\nAccording to whether the observation is made in a plane normal to the\nmagnetic field or in the same direction, the line transforms itself\ninto a triplet or doublet, and the new lines are polarized\nrectilinearly or circularly.\n\nThese are the precise phenomena which the calculation foretells: the\nanalysis of the modifications undergone by the light supplies,\nmoreover, valuable information on the electron itself. From the\ndirection of the circular vibrations of the greatest frequency we can\ndetermine the sign of the electric charge in motion and we find it to\nbe negative. But, further than this, from the variation of the period\nwe can calculate the relation of the force acting on the electron to\nits material mass, and, in addition, the relation of the charge to the\nmass. We then find for this relation precisely that value which we\nhave already met with so many times. Such a coincidence cannot be\nfortuitous, and we have the right to believe that the electron\nrevealed by the luminous wave which emanates from it, is really the\nsame as the one made known to us by the study of the cathode rays and\nof the radioactive substances.\n\nHowever, the elementary theory does not suffice to interpret the\ncomplications which later experiments have revealed. The physicists\nmost qualified to effect measurements in these delicate optical\nquestions--M. Cornu, Mr Preston, M. Cotton, MM. Becquerel and\nDeslandres, M. Broca, Professor Michelson, and others--have pointed\nout some remarkable peculiarities. Thus in some cases the number of\nthe component rays dissociated by the magnetic field may be very\nconsiderable.\n\nThe great modification brought to a radiation by the Zeeman effect\nmay, besides, combine itself with other phenomena, and alter the light\nin a still more complicated manner. A pencil of polarized light, as\ndemonstrated by Signori Macaluzo and Corbino, undergoes, in a magnetic\nfield, modifications with regard to absorption and speed of\npropagation.\n\nSome ingenious researches by M. Becquerel and M. Cotton have perfectly\nelucidated all these complications from an experimental point of view.\nIt would not be impossible to link together all these phenomena\nwithout adopting the electronic hypothesis, by preserving the old\noptical equations as modified by the terms relating to the action of\nthe magnetic field. This has actually been done in some very\nremarkable work by M. Voigt, but we may also, like Professor Lorentz,\nlook for more general theories, in which the essential image of the\nelectrons shall be preserved, and which will allow all the facts\nrevealed by experiment to be included.\n\nWe are thus led to the supposition that there is not in the atom one\nvibrating electron only, but that there is to be found in it a\ndynamical system comprising several material points which may be\nsubjected to varied movements. The neutral atom may therefore be\nconsidered as composed of an immovable principal portion positively\ncharged, round which move, like satellites round a planet, several\nnegative electrons of very inferior mass. This conclusion leads us to\nan interpretation in agreement with that which other phenomena have\nalready suggested.\n\nThese electrons, which thus have a variable velocity, generate around\nthemselves a transverse electromagnetic wave which is propagated with\nthe velocity of light; for the charged particle becomes, as soon as it\nexperiences a change of speed, the centre of a radiation. Thus is\nexplained the phenomenon of the emission of radiations. In the same\nway, the movement of electrons may be excited or modified by the\nelectrical forces which exist in any pencil of light they receive, and\nthis pencil may yield up to them a part of the energy it is carrying.\nThis is the phenomenon of absorption.\n\nProfessor Lorentz has not contented himself with thus explaining all\nthe mechanism of the phenomena of emission and absorption. He has\nendeavoured to rediscover, by starting with the fundamental\nhypothesis, the quantitative laws discovered by thermodynamics. He\nsucceeds in showing that, agreeably to the law of Kirchhoff, the\nrelation between the emitting and the absorbing power must be\nindependent of the special properties of the body under observation,\nand he thus again meets with the laws of Planck and of Wien:\nunfortunately the calculation can only be made in the case of great\nwave-lengths, and grave difficulties exist. Thus it cannot be very\nclearly explained why, by heating a body, the radiation is displaced\ntowards the side of the short wave-lengths, or, if you will, why a\nbody becomes luminous from the moment its temperature has reached a\nsufficiently high degree. On the other hand, by calculating the energy\nof the vibrating particles we are again led to attribute to these\nparticles the same constitution as that of the electrons.\n\nIt is in the same way possible, as Professor Lorentz has shown, to\ngive a very satisfactory explanation of the thermo-electric phenomena\nby supposing that the number of liberated electrons which exist in a\ngiven metal at a given temperature has a determined value varying with\neach metal, and is, in the case of each body, a function of the\ntemperature. The formula obtained, which is based on these hypotheses,\nagrees completely with the classic results of Clausius and of Lord\nKelvin. Finally, if we recollect that the phenomena of electric and\ncalorific conductivity are perfectly interpreted by the hypothesis of\nelectrons, it will no longer be possible to contest the importance of\na theory which allows us to group together in one synthesis so many\nfacts of such diverse origins.\n\nIf we study the conditions under which a wave excited by an electron's\nvariations in speed can be transmitted, they again bring us face to\nface, and generally, with the results pointed out by the ordinary\nelectromagnetic theory. Certain peculiarities, however, are not\nabsolutely the same. Thus the theory of Lorentz, as well as that of\nMaxwell, leads us to foresee that if an insulating mass be caused to\nmove in a magnetic field normally to its lines of force, a\ndisplacement will be produced in this mass analogous to that of which\nFaraday and Maxwell admitted the existence in the dielectric of a\ncharged condenser. But M.H. Poincare has pointed out that, according\nas we adopt one or other of these authors' points of view, so the\nvalue of the displacement differs. This remark is very important, for\nit may lead to an experiment which would enable us to make a definite\nchoice between the two theories.\n\nTo obtain the displacement estimated according to Lorentz, we must\nmultiply the displacement calculated according to Hertz by a factor\nrepresenting the relation between the difference of the specific\ninductive capacities of the dielectric and of a vacuum, and the first\nof these powers. If therefore we take as dielectric the air of which\nthe specific inductive capacity is perceptibly the same as that of a\nvacuum, the displacement, according to the idea of Lorentz, will be\nnull; while, on the contrary, according to Hertz, it will have a\nfinite value. M. Blondlot has made the experiment. He sent a current\nof air into a condenser placed in a magnetic field, and was never able\nto notice the slightest trace of electrification. No displacement,\ntherefore, is effected in the dielectric. The experiment being a\nnegative one, is evidently less convincing than one giving a positive\nresult, but it furnishes a very powerful argument in favour of the\ntheory of Lorentz.\n\nThis theory, therefore, appears very seductive, yet it still raises\nobjections on the part of those who oppose to it the principles of\nordinary mechanics. If we consider, for instance, a radiation emitted\nby an electron belonging to one material body, but absorbed by another\nelectron in another body, we perceive immediately that, the\npropagation not being instantaneous, there can be no compensation\nbetween the action and the reaction, which are not simultaneous; and\nthe principle of Newton thus seems to be attacked. In order to\npreserve its integrity, it has to be admitted that the movements in\nthe two material substances are compensated by that of the ether which\nseparates these substances; but this conception, although in tolerable\nagreement with the hypothesis that the ether and matter are not of\ndifferent essence, involves, on a closer examination, suppositions\nhardly satisfactory as to the nature of movements in the ether.\n\nFor a long time physicists have admitted that the ether as a whole\nmust be considered as being immovable and capable of serving, so to\nspeak, as a support for the axes of Galileo, in relation to which axes\nthe principle of inertia is applicable,--or better still, as M.\nPainleve has shown, they alone allow us to render obedience to the\nprinciple of causality.\n\nBut if it were so, we might apparently hope, by experiments in\nelectromagnetism, to obtain absolute motion, and to place in evidence\nthe translation of the earth relatively to the ether. But all the\nresearches attempted by the most ingenious physicists towards this end\nhave always failed, and this tends towards the idea held by many\ngeometricians that these negative results are not due to imperfections\nin the experiments, but have a deep and general cause. Now Lorentz has\nendeavoured to find the conditions in which the electromagnetic theory\nproposed by him might agree with the postulate of the complete\nimpossibility of determining absolute motion. It is necessary, in\norder to realise this concord, to imagine that a mobile system\ncontracts very slightly in the direction of its translation to a\ndegree proportioned to the square of the ratio of the velocity of\ntransport to that of light. The electrons themselves do not escape\nthis contraction, although the observer, since he participates in the\nsame motion, naturally cannot notice it. Lorentz supposes, besides,\nthat all forces, whatever their origin, are affected by a translation\nin the same way as electromagnetic forces. M. Langevin and M. H.\nPoincare have studied this same question and have noted with precision\nvarious delicate consequences of it. The singularity of the hypotheses\nwhich we are thus led to construct in no way constitutes an argument\nagainst the theory of Lorentz; but it has, we must acknowledge,\ndiscouraged some of the more timid partisans of this theory.[48]\n\n[Footnote 48: An objection not here noticed has lately been formulated\nwith much frankness by Professor Lorentz himself. It is one of the\npillars of his theory that only the negative electrons move when an\nelectric current passes through a metal, and that the positive\nelectrons (if any such there be) remain motionless. Yet in the\nexperiment known as Hall's, the current is deflected by the magnetic\nfield to one side of the strip in certain metals, and to the opposite\nside in others. This seems to show that in certain cases the positive\nelectrons move instead of the negative, and Professor Lorentz\nconfesses that up to the present he can find no valid argument against\nthis. See _Archives Neerlandaises_ 1906, parts 1 and 2.--ED.]\n\n\nSec. 3. THE MASS OF ELECTRONS\n\nOther conceptions, bolder still, are suggested by the results of\ncertain interesting experiments. The electron affords us the\npossibility of considering inertia and mass to be no longer a\nfundamental notion, but a consequence of the electromagnetic\nphenomena.\n\nProfessor J.J. Thomson was the first to have the clear idea that a\npart, at least, of the inertia of an electrified body is due to its\nelectric charge. This idea was taken up and precisely stated by\nProfessor Max Abraham, who, for the first time, was led to regard\nseriously the seemingly paradoxical notion of mass as a function of\nvelocity. Consider a small particle bearing a given electric charge,\nand let us suppose that this particle moves through the ether. It is,\nas we know, equivalent to a current proportional to its velocity, and\nit therefore creates a magnetic field the intensity of which is\nlikewise proportional to its velocity: to set it in motion, therefore,\nthere must be communicated to it over and above the expenditure\ncorresponding to the acquisition of its ordinary kinetic energy, a\nquantity of energy proportional to the square of its velocity.\nEverything, therefore, takes place as if, by the fact of\nelectrification, its capacity for kinetic energy and its material mass\nhad been increased by a certain constant quantity. To the ordinary\nmass may be added, if you will, an electromagnetic mass.\n\nThis is the state of things so long as the speed of the translation of\nthe particle is not very great, but they are no longer quite the same\nwhen this particle is animated with a movement whose rapidity becomes\ncomparable to that with which light is propagated.\n\nThe magnetic field created is then no longer a field in repose, but\nits energy depends, in a complicated manner, on the velocity, and the\napparent increase in the mass of the particle itself becomes a\nfunction of the velocity. More than this, this increase may not be the\nsame for the same velocity, but varies according to whether the\nacceleration is parallel with or perpendicular to the direction of\nthis velocity. In other words, there seems to be a longitudinal; and a\ntransversal mass which need not be the same.\n\nAll these results would persist even if the material mass were very\nsmall relatively to the electromagnetic mass; and the electron\npossesses some inertia even if its ordinary mass becomes slighter and\nslighter. The apparent mass, it can be easily shown, increases\nindefinitely when the velocity with which the electrified particle is\nanimated tends towards the velocity of light, and thus the work\nnecessary to communicate such a velocity to an electron would be\ninfinite. It is in consequence impossible that the speed of an\nelectron, in relation to the ether, can ever exceed, or even\npermanently attain to, 300,000 kilometres per second.\n\nAll the facts thus predicted by the theory are confirmed by\nexperiment. There is no known process which permits the direct\nmeasurement of the mass of an electron, but it is possible, as we have\nseen, to measure simultaneously its velocity and the relation of the\nelectric charge to its mass. In the case of the cathode rays emitted\nby radium, these measurements are particularly interesting, for the\nreason that the rays which compose a pencil of cathode rays are\nanimated by very different speeds, as is shown by the size of the\nstain produced on a photographic plate by a pencil of them at first\nvery constricted and subsequently dispersed by the action of an\nelectric or magnetic field. Professor Kaufmann has effected some very\ncareful experiments by a method he terms the method of crossed\nspectra, which consists in superposing the deviations produced by a\nmagnetic and an electric field respectively acting in directions at\nright angles one to another. He has thus been enabled by working _in\nvacuo_ to register the very different velocities which, starting in\nthe case of certain rays from about seven-tenths of the velocity of\nlight, attain in other cases to ninety-five hundredths of it.\n\nIt is thus noted that the ratio of charge to mass--which for ordinary\nspeeds is constant and equal to that already found by so many\nexperiments--diminishes slowly at first, and then very rapidly when\nthe velocity of the ray increases and approaches that of light. If we\nrepresent this variation by a curve, the shape of this curve inclines\nus to think that the ratio tends toward zero when the velocity tends\ntowards that of light.\n\nAll the earlier experiments have led us to consider that the electric\ncharge was the same for all electrons, and it can hardly be conceived\nthat this charge can vary with the velocity. For in order that the\nrelation, of which one of the terms remains fixed, should vary, the\nother term necessarily cannot remain constant. The experiments of\nProfessor Kaufmann, therefore, confirm the previsions of Max Abraham's\ntheory: the mass depends on the velocity, and increases indefinitely\nin proportion as this velocity approaches that of light. These\nexperiments, moreover, allow the numerical results of the calculation\nto be compared with the values measured. This very satisfactory\ncomparison shows that the apparent total mass is sensibly equal to the\nelectromagnetic mass; the material mass of the electron is therefore\nnil, and the whole of its mass is electromagnetic.\n\nThus the electron must be looked upon as a simple electric charge\ndevoid of matter. Previous examination has led us to attribute to it a\nmass a thousand times less that that of the atom of hydrogen, and a\nmore attentive study shows that this mass was fictitious. The\nelectromagnetic phenomena which are produced when the electron is set\nin motion or a change effected in its velocity, simply have the\neffect, as it were, of simulating inertia, and it is the inertia due\nto the charge which has caused us to be thus deluded.\n\nThe electron is therefore simply a small volume determined at a point\nin the ether, and possessing special properties;[49] this point is\npropagated with a velocity which cannot exceed that of light. When\nthis velocity is constant, the electron creates around it in its\npassage an electric and a magnetic field; round this electrified\ncentre there exists a kind of wake, which follows it through the ether\nand does not become modified so long as the velocity remains\ninvariable. If other electrons follow the first within a wire, their\npassage along the wire will be what is called an electric current.\n\n[Footnote 49: This cannot be said to be yet completely proved. _Cf_.\nSir Oliver Lodge, _Electrons_, London, 1906, p. 200.--ED.]\n\nWhen the electron is subjected to an acceleration, a transverse wave\nis produced, and an electromagnetic radiation is generated, of which\nthe character may naturally change with the manner in which the speed\nvaries. If the electron has a sufficiently rapid periodical movement,\nthis wave is a light wave; while if the electron stops suddenly, a\nkind of pulsation is transmitted through the ether, and thus we obtain\nRoentgen rays.\n\n\nSec. 4. NEW VIEWS ON THE CONSTITUTION OF THE ETHER AND OF MATTER\n\nNew and valuable information is thus afforded us regarding the\nproperties of the ether, but will this enable us to construct a\nmaterial representation of this medium which fills the universe, and\nso to solve a problem which has baffled, as we have seen, the\nprolonged efforts of our predecessors?\n\nCertain scholars seem to have cherished this hope. Dr. Larmor in\nparticular, as we have seen, has proposed a most ingenious image, but\none which is manifestly insufficient. The present tendency of\nphysicists rather tends to the opposite view; since they consider\nmatter as a very complex object, regarding which we wrongly imagine\nourselves to be well informed because we are so much accustomed to it,\nand its singular properties end by seeming natural to us. But in all\nprobability the ether is, in its objective reality, much more simple,\nand has a better right to be considered as fundamental.\n\nWe cannot therefore, without being very illogical, define the ether by\nmaterial properties, and it is useless labour, condemned beforehand to\nsterility, to endeavour to determine it by other qualities than those\nof which experiment gives us direct and exact knowledge.\n\nThe ether is defined when we know, in all its points, and in magnitude\nand in direction, the two fields, electric and magnetic, which may\nexist in it. These two fields may vary; we speak from habit of a\nmovement propagated in the ether, but the phenomenon within the reach\nof experiment is the propagation of these variations.\n\nSince the electrons, considered as a modification of the ether\nsymmetrically distributed round a point, perfectly counterfeit that\ninertia which is the fundamental property of matter, it becomes very\ntempting to suppose that matter itself is composed of a more or less\ncomplex assemblage of electrified centres in motion.\n\nThis complexity is, in general, very great, as is demonstrated by the\nexamination of the luminous spectra produced by the atoms, and it is\nprecisely because of the compensations produced between the different\nmovements that the essential properties of matter--the law of the\nconservation of inertia, for example--are not contrary to the\nhypothesis.\n\nThe forces of cohesion thus would be due to the mutual attractions\nwhich occur in the electric and magnetic fields produced in the\ninterior of bodies; and it is even conceivable that there may be\nproduced, under the influence of these actions, a tendency to\ndetermine orientation, that is to say, that a reason can be seen why\nmatter may be crystallised.[50]\n\n[Footnote 50: The reader should, however, be warned that a theory has\nlately been put forth which attempts to account for crystallisation on\npurely mechanical grounds. See Messrs Barlow and Pope's \"Development\nof the Atomic Theory\" in the _Transactions of the Chemical Society_,\n1906.--ED.]\n\nAll the experiments effected on the conductivity of gases or metals,\nand on the radiations of active bodies, have induced us to regard the\natom as being constituted by a positively charged centre having\npractically the same magnitude as the atom itself, round which the\nelectrons gravitate; and it might evidently be supposed that this\npositive centre itself preserves the fundamental characteristics of\nmatter, and that it is the electrons alone which no longer possess any\nbut electromagnetic mass.\n\nWe have but little information concerning these positive particles,\nthough they are met with in an isolated condition, as we have seen, in\nthe canal rays or in the X rays.[51] It has not hitherto been possible\nto study them so successfully as the electrons themselves; but that\ntheir magnitude causes them to produce considerable perturbations in\nthe bodies on which they fall is manifest by the secondary emissions\nwhich complicate and mask the primitive phenomenon. There are,\nhowever, strong reasons for thinking that these positive centres are\nnot simple. Thus Professor Stark attributes to them, with experiments\nin proof of his opinion, the emission of the spectra of the rays in\nGeissler tubes, and the complexity of the spectrum discloses the\ncomplexity of the centre. Besides, certain peculiarities in the\nconductivity of metals cannot be explained without a supposition of\nthis kind. So that the atom, deprived of the cathode corpuscle, would\nbe still liable to decomposition into elements analogous to electrons\nand positively charged. Consequently nothing prevents us supposing\nthat this centre likewise simulates inertia by its electromagnetic\nproperties, and is but a condition localised in the ether.\n\n[Footnote 51: There is much reason for thinking that the canal rays do\nnot contain positive particles alone, but are accompanied by negative\nelectrons of slow velocity. The X rays are thought, as has been said\nabove, to contain neither negative nor positive particles, but to be\nmerely pulses in the ether.--ED.]\n\nHowever this may be, the edifice thus constructed, being composed of\nelectrons in periodical motion, necessarily grows old. The electrons\nbecome subject to accelerations which produce a radiation towards the\nexterior of the atom; and certain of them may leave the body, while\nthe primitive stability is, in the end, no longer assured, and a new\narrangement tends to be formed. Matter thus seems to us to undergo\nthose transformations of which the radio-active bodies have given us\nsuch remarkable examples.\n\nWe have already had, in fragments, these views on the constitution of\nmatter; a deeper study of the electron thus enables us to take up a\nposition from which we obtain a sharp, clear, and comprehensive grasp\nof the whole and a glimpse of indefinite horizons.\n\nIt would be advantageous, however, in order to strengthen this\nposition, that a few objections which still menace it should be\nremoved. The instability of the electron is not yet sufficiently\ndemonstrated. How is it that its charge does not waste itself away,\nand what bonds assure the permanence of its constitution?\n\nOn the other hand, the phenomena of gravitation remain a mystery.\nLorentz has endeavoured to build up a theory in which he explains\nattraction by supposing that two charges of similar sign repel each\nother in a slightly less degree than that in which two charges, equal\nbut of contrary sign, attract each other, the difference being,\nhowever, according to the calculation, much too small to be directly\nobserved. He has also sought to explain gravitation by connecting it\nwith the pressures which may be produced on bodies by the vibratory\nmovements which form very penetrating rays. Recently M. Sutherland has\nimagined that attraction is due to the difference of action in the\nconvection currents produced by the positive and negative corpuscles\nwhich constitute the atoms of the stars, and are carried along by the\nastronomical motions. But these hypotheses remain rather vague, and\nmany authors think, like M. Langevin, that gravitation must result\nfrom some mode of activity of the ether totally different from the\nelectromagnetic mode.\n\n\n\n\nCHAPTER XI\n\nTHE FUTURE OF PHYSICS\n\n\nIt would doubtless be exceedingly rash, and certainly very\npresumptuous, to seek to predict the future which may be reserved for\nphysics. The role of prophet is not a scientific one, and the most\nfirmly established previsions of to-day may be overthrown by the\nreality of to-morrow.\n\nNevertheless, the physicist does not shun an extrapolation of some\nlittle scope when it is not too far from the realms of experiment; the\nknowledge of the evolution accomplished of late years authorises a few\nsuppositions as to the direction in which progress may continue.\n\nThe reader who has deigned to follow me in the rapid excursion we have\njust made through the domain of the science of Nature, will doubtless\nbring back with him from his short journey the general impression that\nthe ancient limits to which the classic treatises still delight in\nrestricting the divers chapters of physics, are trampled down in all\ndirections.\n\nThe fine straight roads traced out by the masters of the last century,\nand enlarged and levelled by the labour of such numbers of workmen,\nare now joined together by a crowd of small paths which furrow the\nfield of physics. It is not only because they cover regions as yet\nlittle explored where discoveries are more abundant and more easy,\nthat these cross-cuts are so frequent, but also because a higher hope\nguides the seekers who engage in these new routes.\n\nIn spite of the repeated failures which have followed the numerous\nattempts of past times, the idea has not been abandoned of one day\nconquering the supreme principle which must command the whole of\nphysics.\n\nSome physicists, no doubt, think such a synthesis to be impossible of\nrealisation, and that Nature is infinitely complex; but,\nnotwithstanding all the reserves they may make, from the philosophical\npoint of view, as to the legitimacy of the process, they do not\nhesitate to construct general hypotheses which, in default of complete\nmental satisfaction, at least furnish them with a highly convenient\nmeans of grouping an immense number of facts till then scattered\nabroad.\n\nTheir error, if error there be, is beneficial, for it is one of those\nthat Kant would have classed among the fruitful illusions which\nengender the indefinite progress of science and lead to great and\nimportant co-ordinations.\n\nIt is, naturally, by the study of the relations existing between\nphenomena apparently of very different orders that there can be any\nhope of reaching the goal; and it is this which justifies the peculiar\ninterest accorded to researches effected in the debatable land between\ndomains hitherto considered as separate.\n\nAmong all the theories lately proposed, that of the ions has taken a\npreponderant place; ill understood at first by some, appearing\nsomewhat singular, and in any case useless, to others, it met at its\ninception, in France at least, with only very moderate favour.\n\nTo-day things have greatly changed, and those even who ignored it have\nbeen seduced by the curious way in which it adapts itself to the\ninterpretation of the most recent experiments on very different\nsubjects. A very natural reaction has set in; and I might almost say\nthat a question of fashion has led to some exaggerations.\n\nThe electron has conquered physics, and many adore the new idol rather\nblindly. Certainly we can only bow before an hypothesis which enables\nus to group in the same synthesis all the discoveries on electric\ndischarges and on radioactive substances, and which leads to a\nsatisfactory theory of optics and of electricity; while by the\nintermediary of radiating heat it seems likely to embrace shortly the\nprinciples of thermodynamics also. Certainly one must admire the power\nof a creed which penetrates also into the domain of mechanics and\nfurnishes a simple representation of the essential properties of\nmatter; but it is right not to lose sight of the fact that an image\nmay be a well-founded appearance, but may not be capable of being\nexactly superposed on the objective reality.\n\nThe conception of the atom of electricity, the foundation of the\nmaterial atoms, evidently enables us to penetrate further into\nNature's secrets than our predecessors; but we must not be satisfied\nwith words, and the mystery is not solved when, by a legitimate\nartifice, the difficulty has simply been thrust further back. We have\ntransferred to an element ever smaller and smaller those physical\nqualities which in antiquity were attributed to the whole of a\nsubstance; and then we shifted them later to those chemical atoms\nwhich, united together, constitute this whole. To-day we pass them on\nto the electrons which compose these atoms. The indivisible is thus\nrendered, in a way, smaller and smaller, but we are still unacquainted\nwith what its substance may be. The notion of an electric charge which\nwe substitute for that of a material mass will permit phenomena to be\nunited which we thought separate, but it cannot be considered a\ndefinite explanation, or as the term at which science must stop. It is\nprobable, however, that for a few years still physics will not travel\nbeyond it. The present hypothesis suffices for grouping known facts,\nand it will doubtless enable many more to be foreseen, while new\nsuccesses will further increase its possessions.\n\nThen the day will arrive when, like all those which have shone before\nit, this seductive hypothesis will lead to more errors than\ndiscoveries. It will, however, have been improved, and it will have\nbecome a very vast and very complete edifice which some will not\nwillingly abandon; for those who have made to themselves a comfortable\ndwelling-place on the ruins of ancient monuments are often too loth to\nleave it.\n\nIn that day the searchers who were in the van of the march after truth\nwill be caught up and even passed by others who will have followed a\nlonger, but perhaps surer road. We also have seen at work those\nprudent physicists who dreaded too daring creeds, and who sought only\nto collect all the documentary evidence possible, or only took for\ntheir guide a few principles which were to them a simple\ngeneralisation of facts established by experiments; and we have been\nable to prove that they also were effecting good and highly useful\nwork.\n\nNeither the former nor the latter, however, carry out their work in an\nisolated way, and it should be noted that most of the remarkable\nresults of these last years are due to physicists who have known how\nto combine their efforts and to direct their activity towards a common\nobject, while perhaps it may not be useless to observe also that\nprogress has been in proportion to the material resources of our\nlaboratories.\n\nIt is probable that in the future, as in the past, the greatest\ndiscoveries, those which will suddenly reveal totally unknown regions,\nand open up entirely new horizons, will be made by a few scholars of\ngenius who will carry on their patient labour in solitary meditation,\nand who, in order to verify their boldest conceptions, will no doubt\ncontent themselves with the most simple and least costly experimental\napparatus. Yet for their discoveries to yield their full harvest, for\nthe domain to be systematically worked and desirable results obtained,\nthere will be more and more required the association of willing minds,\nthe solidarity of intelligent scholars, and it will be also necessary\nfor these last to have at their disposal the most delicate as well as\nthe most powerful instruments. These are conditions paramount at the\npresent day for continuous progress in experimental science.\n\nIf, as has already happened, unfortunately, in the history of science,\nthese conditions are not complied with; if the freedoms of the workers\nare trammelled, their unity disturbed, and if material facilities are\ntoo parsimoniously afforded them,--evolution, at present so rapid, may\nbe retarded, and those retrogressions which, by-the-by, have been\nknown in all evolutions, may occur, although even then hope in the\nfuture would not be abolished for ever.\n\nThere are no limits to progress, and the field of our investigations\nhas no boundaries. Evolution will continue with invincible force. What\nwe to-day call the unknowable, will retreat further and further before\nscience, which will never stay her onward march. Thus physics will\ngive greater and increasing satisfaction to the mind by furnishing new\ninterpretations of phenomena; but it will accomplish, for the whole of\nsociety, more valuable work still, by rendering, by the improvements\nit suggests, life every day more easy and more agreeable, and by\nproviding mankind with weapons against the hostile forces of Nature.","title":"The New Physics and Its Evolution","tradition":"philosophy-ethics","translated_text":null,"word_count":77242}