,,evolution999999 ,the ,international ,scientific ,series ,,the ,,new ,,physics ,,and ,,its ,,evolution by ,,lucien ,,poincar ,inspctur-,general de l',instruction ,publique ,being the ,authorized ,translation of ,,la ,,physique ,,moderne1 ,,son ,,volution ,new ,york ,d4 ,appleton and ,company #aiji ,prefatory ,note ,m4 ,lucien ,poincar is one of the distinguished family of mathematicians which has during the last few years given a ,minister of ,finance to the ,republic and a ,president to the ,acadmie des ,sciences4 ,he is also one of the nineteen ,inspectors-,general of ,public ,instruction who are charged with the duty of visiting the different universities and lyces in ,france and of reporting upon the state of the studies there pursued4 ,hence he is in an excellent position to appreciate at its proper value the extraordinary change which has lately revolutionized physical science1 while his official position has kept him aloof from the controversies aroused by the discovery of radium and by recent speculations on the constitution of matter4 ,m4 ,poincar's object and method in writing the book are sufficiently explained in the preface which follows2 but it may be remarked that the best of methods has its defects1 and the excessive condensation which has alone made it possible to include the last decade's discoveries in physical science within a compass of some #cjj pages has1 perhaps1 made the facts here noted assimilable with difficulty by the untrained reader4 ,to remedy this as far as possible1 ,i have prefixed to the present translation a table of contents so extended as to form a fairly complete digest of the book1 while full indexes of authors and subjects have also been added4 ,the few notes necessary either for better elucidation of the terms employed1 or for giving account of discoveries made while these pages were passing through the press1 may be distinguished from the author's own by the signature ,,ed4 ,,the ,,editor4 ,,royal ,,institution ,,of ,,great ,,britain1 ,april #aijg4 ,author's ,preface ,during the last ten years so many works have accumulated in the domain of ,physics1 and so many new theories have been propounded1 that those who follow with interest the progress of science1 and even some professed scholars1 absorbed as they are in their own special studies1 find themselves at sea in a confusion more apparent than real4 ,it has therefore occurred to me that it might be useful to write a book which1 while avoiding too great insistence on purely technical details1 should try to make known the general results at which physicists have lately arrived1 and to indicate the direction and import which should be ascribed to those speculations on the constitution of matter1 and the discussions on the nature of first principles1 to which it has become1 so to speak1 the fashion of the present day to devote oneself4 ,i have endeavoured throughout to rely only on the experiments in which we can place the most confidence1 and1 above all1 to show how the ideas prevailing at the present day have been formed1 by tracing their evolution1 and rapidly examining the successive transformations which have brought them to their present condition4 ,in order to understand the text1 the reader will have no need to consult any treatise on physics1 for ,i have throughout given the necessary definitions and set forth the fundamental facts4 ,moreover1 while strictly employing exact expressions1 ,i have avoided the use of mathematical language4 ,algebra is an admirable tongue1 but there are many occasions where it can only be used with much discretion4 ,nothing would be easier than to point out many great omissions from this little volume2 but some1 at all events1 are not involuntary4 ,certain questions which are still too confused have been put on one side1 as have a few others which form an important collection for a special study to be possibly made later4 ,thus1 as regards electrical phenomena1 the relations between electricity and optics1 as also the theories of ionization1 the electronic hypothesis1 etc41 have been treated at some length2 but it has not been thought necessary to dilate upon the modes of production and utilization of the current1 upon the phenomena of magnetism1 or upon all the applications which belong to the domain of ,electrotechnics4 ,l4 ,,poincar4 ,contents ,,editor',s ,,prefatory ,,note ,,author',s ,,preface ,,table ,,of ,,contents ,,chapter ,i ,,the ,,evolution ,,of ,,physics ,revolutionary change in modern ,physics only apparent3 evolution not revolution the rule in ,physical ,theory-- ,revival of metaphysical speculation and influence of ,descartes3 all phenomena reduced to matter and movement-- ,modern physicists challenge this3 physical1 unlike mechanical1 phenomena seldom reversible--,two schools1 one considering experimental laws imperative1 the other merely studying relations of magnitudes3 both teach something of truth--,third or eclectic school-- ,is mechanics a branch of electrical science8 ,,chapter ,,ii ,,measurements #a4 ,metrology3 ,lord ,kelvin's view of its necessity-- ,its definition #b4 ,the ,measure of ,length3 ,necessity for unit-- ,absolute length--,history of ,standard--,description of ,standard ,metre--,unit of wave-lengths preferable--,the ,international ,metre #c4 ,the ,measure of ,mass3 ,distinction between mass and weight--,objections to legal kilogramme and its precision--,possible improvement #d4 ,the ,measure of ,time3 ,unit of time the second--,alternative units proposed--,improvements in chronometry and invar #e4 ,the ,measure of ,temperature3 ,fundamental and derived units--,ordinary unit of temperature purely arbitrary--,absolute unit mass of ,h at pressure of #a m4 of ,hg at #j ,c4--,divergence of thermometric and thermodynamic scales--,helium thermometer for low1 thermo-electric couple for high1 temperatures--,lummer and ,pringsheim's improvements in thermometry4 #f4 ,derived ,units and ,measure of ,energy3 ,importance of erg as unit--,calorimeter usual means of determination--,photometric units4 #g4 ,measure of ,physical ,constants3 ,constant of gravitation--,discoveries of ,cavendish1 ,vernon ,boys1 ,etvs1 ,richarz and ,krigar-,menzel--,michelson's improvements on ,fizeau and ,foucault's experiments-- ,measure of speed of light4 ,,chapter ,,iii ,,principles #a4 ,the ,principles of ,physics3 ,the ,principles of ,mechanics affected by recent discoveries--,is mass indestructible8--,landolt and ,heydweiller's experiments --,lavoisier's law only approximately true--,curie's principle of symmetry4 #b4 ,the ,principle of the ,conservation of ,energy3 ,its evolution3 ,bernoulli1 ,lavoisier and ,laplace1 ,young1 ,rumford1 ,davy1 ,sadi ,carnot1 and ,robert ,mayer--,mayer's drawbacks--,error of those who would make mechanics part of energetics--,verdet's predictions--,rankine inventor of energetics--,usefulness of ,work as standard form of energy--,physicists who think matter form of energy-- ,objections to this--,philosophical value of conservation doctrine4 #c4 ,the ,principle of ,carnot and ,clausius3 ,originality of ,carnot's principle that fall of temperature necessary for production of work by heat-- ,clausius' postulate that heat cannot pass from cold to hot body without accessory phenomena--,entropy result of this--,definition of entropy--,entropy tends to increase incessantly--,a magnitude which measures evolution of system--,clausius' and ,kelvin's deduction that heat end of all energy in ,universe--,objection to this-- ,carnot's principle not necessarily referable to mechanics --,brownian movements--,lippmann's objection to kinetic hypothesis4 #d4 ,thermodynamics3 ,historical work of ,massieu1 ,willard ,gibbs1 ,helmholtz1 and ,duhem--,willard ,gibbs founder of thermodynamic statics1 ,van t',hoff its reviver--,the ,phase ,law--,raveau explains it without thermodynamics4 #e4 ,atomism3 ,connection of subject with preceding ,hannequin's essay on the atomic hypothesis--,molecular physics in disfavour--,surface-tension1 etc41 vanishes when molecule reached--,size of molecule--,kinetic theory of gases--,willard ,gibbs and ,boltzmann introduce into it law of probabilities--,mean free path of gaseous molecules--,application to optics--,final division of matter4 ,,chapter ,,iv ,,the ,,various ,,states ,,of ,,matter #a4 ,the ,statics of ,fluids3 ,researches of ,andrews1 ,cailletet1 and others on liquid and gaseous states-- ,amagat's experiments--,van der ,waals' equation--,discovery of corresponding states--,amagat's superposed diagrams--,exceptions to law--,statics of mixed fluids-- ,kamerlingh ,onnes' researches--,critical ,constants-- ,characteristic equation of fluid not yet ascertainable4 #b4 ,the ,liquefaction of ,gases and ,low ,temperatures3 ,linde's1 ,siemens'1 and ,claude's methods of liquefying gases--,apparatus of ,claude described--,dewar's experiments--,modification of electrical properties of matter by extreme cold3 of magnetic and chemical-- ,vitality of bacteria unaltered--,ramsay's discovery of rare gases of atmosphere--,their distribution in nature--,liquid hydrogen--,helium4 #c4 ,solids and ,liquids3 ,continuity of ,solid and ,liquid ,states--,viscosity common to both--,also ,rigidity-- ,spring's analogies of solids and liquids--,crystallization --,lehmann's liquid crystals--,their existence doubted --,tamman's view of discontinuity between crystalline and liquid states4 #d4 ,the ,deformation of ,solids3 ,elasticity-- ,hoocke's1 ,bach's1 and ,bouasse's researches--,voigt on the elasticity of crystals--,elastic and permanent deformations--,brillouin's states of unstable equilibria--,duhem and the thermodynamic postulates-- ,experimental confirmation--,guillaume's researches on nickel steel--,alloys4 ,,chapter ,v ,,solutions ,,and ,,electrolytic ,,dissociation #a4 ,solution3 ,kirchhoff's1 ,gibb's1 ,duhem's and ,van t',hoff's researches4 #b4 ,osmosis3 ,history of phenomenon--,traube and biologists establish existence of semi-permeable walls--,villard's experiments with gases--,pfeffer shows osmotic pressure proportional to concentration-- ,disagreement as to cause of phenomenon4 #c4 ,osmosis applied to ,solution3 ,van t',hoff's discoveries--,analogy between dissolved body and perfect gas--,faults in analogy4 #d4 ,electrolytic ,dissociation3 ,van t',hoff's and ,arrhenius' researches--,ionic hypothesis of--,fierce opposition to at first--,arrhenius' ideas now triumphant --,advantages of ,arrhenius' hypothesis--,the ions which react--,ostwald's conclusions from this--,nernst's theory of ,electrolysis--,electrolysis of gases makes electronic theory probable--,faraday's two laws--,valency-- ,helmholtz's consequences from ,faraday's laws4 ,,chapter ,,vi ,,the ,,ether #a4 ,the ,luminiferous ,ether3 ,first idea of ,ether due to ,descartes--,ether must be imponderable--,fresnel shows light vibrations to be transverse--,transverse vibrations cannot exist in fluid--,ether must be discontinuous4 #b4 ,radiations3 ,wave-lengths and their measurements--,rubens' and ,lenard's researches-- ,stationary waves and colour-photography--,fresnel's hypothesis opposed by ,neumann--,wiener's and ,cotton's experiments4 #c4 ,the ,electromagnetic ,ether3 ,ampre's advocacy of mathematical expression--,faraday first shows influence of medium in electricity--,maxwell's proof that light-waves electromagnetic--,his unintelligibility--,required confirmation of theory by ,hertz4 #d4 ,electrical ,oscillations3 ,hertz's experiments-- ,blondlot proves electromagnetic disturbance propagated with speed of light--,discovery of ether waves intermediate between ,hertzian and visible ones--,rubens' and ,nichols' experiments--,hertzian and light rays contrasted--,pressure of light4 #e4 ,the ,x-,rays3 ,rntgen's discovery--,properties of ,x-rays--,not homogeneous--,rutherford and ,m',clung's experiments on energy corresponding to--,barkla's experiments on polarisation of--,their speed that of light--,are they merely ultra-violet8--,stokes and ,wiechert's theory of independent pulsations generally preferred--,j4,j4 ,thomson's idea of their formation-- ,sutherland's and ,le ,bon's theories--,the ,n-,rays-- ,blondlot's discovery--,experiments cannot be repeated outside ,france--,gutton and ,mascart's confirmation-- ,negative experiments prove nothing--,supposed wave-length of ,n-rays4 #f4 ,the ,ether and ,gravitation3 ,descartes' and ,newton's ideas on gravitation--,its speed and other extraordinary characteristics--,lesage's hypothesis--,crmieux' experiments with drops of liquids--,hypothesis of ether insufficient4 ,,chapter ,,vii ,,wireless ,,telegraphy #a4 ,histories of wireless telegraphy already written1 and difficulties of the subject4 #b4 ,two systems3 that which uses the material media 7earth1 air1 or water71 and that which employs ether only4 #c4 ,use of earth as return wire by ,steinheil --,morse's experiments with water of canal--,seine used as return wire during siege of ,paris--,johnson and ,melhuish's ,indian experiments--,preece's telegraph over ,bristol ,channel--,he welcomes ,marconi4 #d4 ,early attempts at transmission of messages through ether--,experiments of ,rathenau and others4 #e4 ,forerunners of ether telegraphy3 ,clerk ,maxwell and ,hertz--,dolbear1 ,hughes1 and ,graham ,bell4 #f4 ,telegraphy by ,hertzian waves first suggested by ,threlfall--,crookes'1 ,tesla's1 ,lodge's1 ,rutherford's1 and ,popoff's contributions--,marconi first makes it practicable4 #g4 ,the receiver in wireless telegraphy--,varley's1 ,calzecchi--,onesti's1 and ,branly's researches-- ,explanation of coherer still obscure4 #h4 ,wireless telegraphy enters the commercial stage-- ,defect of ,marconi's system--,braun's1 ,armstrong's1 ,lee de ,forest's1 and ,fessenden's systems make use of earth-- ,hertz and ,marconi entitled to foremost place among discoverers4 ,,chapter ,,viii ,,the ,,conductivity ,,of ,,gases ,,and ,,the ,,ions #a4 ,the ,conductivity of ,gases3 ,relations of matter to ether cardinal problem--,conductivity of gases at first misapprehended--,erman's forgotten researches--,giese first notices phenomenon--,experiment with ,x-rays-- ,j4,j4 ,thomson's interpretation--,ionized gas not obedient to ,ohm's law--,discharge of charged conductors by ionized gas4 #b4 ,the ,condensation of water-vapour by ,ions3 ,vapour will not condense without nucleus--,wilson's experiments on electrical condensation--,wilson and ,thomson's counting experiment--,twenty million ions per c4cm4 of gas--,estimate of charge borne by ion-- ,speed of charges--,zeleny's and ,langevin's experiments--,negative ions #a_/ajjj of size of atoms--,natural unit of electricity or electrons4 #c4 ,how ,ions are ,produced3 ,various causes of ionization--,moreau's experiments with alkaline salts--,barus and ,bloch on ionization by phosphorus vapours--,ionization always result of shock4 #d4 ,electrons in ,metals3 ,movement of electrons in metals foreshadowed by ,weber--,giese's1 ,riecke's1 ,drude's1 and ,j4,j4 ,thomson's researches--,path of ions in metals and conduction of heat--,theory of ,lorentz--,hesehus' explanation of electrification by contact--,emission of electrons by charged body-- ,thomson's measurement of positive ions4 ,,chapter ,,ix ,,cathode ,,rays ,,and ,,radioactive ,,bodies #a4 ,the ,cathode ,rays3 ,history of discovery--,crookes' theory--,lenard rays--,perrin's proof of negative charge--,cathode rays give rise to ,x-rays--,the canal rays--,villard's researches and magneto-cathode rays-- ,ionoplasty--,thomson's measurements of speed of rays-- ,all atoms can be dissociated4 #b4 ,radioactive ,substances3 ,uranic rays of ,niepce de ,st ,victor and ,becquerel--,general radioactivity of matter--,le ,bon's and ,rutherford's comparison of uranic with ,x rays--,pierre and ,mme4 ,curie's discovery of polonium and radium--,their characteristics--,debierne discovers actinium4 #c4 ,radiations and ,emanations of ,radioactive ,bodies3 ,giesel's1 ,becquerel's1 and ,rutherford's ,researches--,alpha1 beta1 and gamma rays--,sagnac's secondary rays--,crookes' spinthariscope--,the emanation --,ramsay and ,soddy's researches upon it--,transformations of radioactive bodies--,their order4 #d4 ,disaggregation of ,matter and ,atomic ,energy3 ,actual transformations of matter in radioactive bodies --,helium or lead final product--,ultimate disappearance of radium from earth--,energy liberated by radium3 its amount and source--,suggested models of radioactive atoms--,generalization from radioactive phenomena -,le ,bon's theories--,ballistic hypothesis generally admitted--,does energy come from without--,sagnac's experiments--,elster and ,geitel's contra4 ,,chapter ,x ,,the ,,ether ,,and ,,matter #a4 ,the ,relations between the ,ether and ,matter3 ,attempts to reduce all matter to forms of ether--,emission and absorption phenomena show reciprocal action-- ,laws of radiation--,radiation of gases--,production of spectrum--,differences between light and sound variations show difference of media--,cauchy's1 ,briot's1 ,carvallo's and ,boussinesq's researches--,helmholtz's and ,poincar's electromagnetic theories of dispersion4 #b4 ,the ,theory of ,lorentz3--,mechanics fails to explain relations between ether and matter--,lorentz predicts action of magnet on spectrum--,zeeman's experiment --,later researches upon ,zeeman effect-- ,multiplicity of electrons--,lorentz's explanation of thermoelectric phenomena by electrons--,maxwell's and ,lorentz's theories do not agree--,lorentz's probably more correct--,earth's movement in relation to ether4 #c4 ,the ,mass of ,electrons3 ,thomson's and ,max ,abraham's view that inertia of charged body due to charge--,longitudinal and transversal mass--,speed of electrons cannot exceed that of light--,ratio of charge to mass and its variation--,electron simple electric charge--,phenomena produced by its acceleration4 #d4 ,new ,views on ,ether and ,matter3 ,insufficiency of ,larmor's view--,ether definable by electric and magnetic fields--,is matter all electrons8 ,atom probably positive centre surrounded by negative electrons--,ignorance concerning positive particles--,successive transformations of matter probable --,gravitation still unaccounted for4 ,,chapter ,,xi ,,the ,,future ,,of ,,physics ,persistence of ambition to discover supreme principle in physics--,supremacy of electron theory at present time--,doubtless destined to disappear like others-- ,constant progress of science predicted--,immense field open before it4 ,,index ,,of ,,names ,,index ,,of ,,subjects ,,chapter ,i ,,the ,,evolution ,,of ,,physics ,the now numerous public which tries with some success to keep abreast of the movement in science1 from seeing its mental habits every day upset1 and from occasionally witnessing unexpected discoveries that produce a more lively sensation from their reaction on social life1 is led to suppose that we live in a really exceptional epoch1 scored by profound crises and illustrated by extraordinary discoveries1 whose singularity surpasses everything known in the past4 ,thus we often hear it said that physics1 in particular1 has of late years undergone a veritable revolution2 that all its principles have been made new1 that all the edifices constructed by our fathers have been overthrown1 and that on the field thus cleared has sprung up the most abundant harvest that has ever enriched the domain of science4 ,it is in fact true that the crop becomes richer and more fruitful1 thanks to the development of our laboratories1 and that the quantity of seekers has considerably increased in all countries1 while their quality has not diminished4 ,we should be sustaining an absolute paradox1 and at the same time committing a crying injustice1 were we to contest the high importance of recent progress1 and to seek to diminish the glory of contemporary physicists4 ,yet it may be as well not to give way to exaggerations1 however pardonable1 and to guard against facile illusions4 ,on closer examination it will be seen that our predecessors might at several periods in history have conceived1 as legitimately as ourselves1 similar sentiments of scientific pride1 and have felt that the world was about to appear to them transformed and under an aspect until then absolutely unknown4 ,let us take an example which is salient enough2 for1 however arbitrary the conventional division of time may appear to a physicist's eyes1 it is natural1 when instituting a comparison between two epochs1 to choose those which extend over a space of half a score of years1 and are separated from each other by the gap of a century4 ,let us1 then1 go back a hundred years and examine what would have been the state of mind of an erudite amateur who had read and understood the chief publications on physical research between #ahjj and #ahaj4 ,let us suppose that this intelligent and attentive spectator witnessed in #ahjj the discovery of the galvanic battery by ,volta4 ,he might from that moment have felt a presentiment that a prodigious transformation was about to occur in our mode of regarding electrical phenomena4 ,brought up in the ideas of ,coulomb and ,franklin1 he might till then have imagined that electricity had unveiled nearly all its mysteries1 when an entirely original apparatus suddenly gave birth to applications of the highest interest1 and excited the blossoming of theories of immense philosophical extent4 ,in the treatises on physics published a little later1 we find traces of the astonishment produced by this sudden revelation of a new world4 ,electricity1 wrote the ,abb ,hay1 enriched by the labour of so many distinguished physicists1 seemed to have reached the term when a science has no further important steps before it1 and only leaves to those who cultivate it the hope of confirming the discoveries of their predecessors1 and of casting a brighter light on the truths revealed4 ,one would have thought that all researches for diversifying the results of experiment were exhausted1 and that theory itself could only be augmented by the addition of a greater degree of precision to the applications of principles already known4 ,while science thus appeared to be making for repose1 the phenomena of the convulsive movements observed by ,galvani in the muscles of a frog when connected by metal were brought to the attention and astonishment of physicists4444 ,volta1 in that ,italy which had been the cradle of the new knowledge1 discovered the principle of its true theory in a fact which reduces the explanation of all the phenomena in question to the simple contact of two substances of different nature4 ,this fact became in his hands the germ of the admirable apparatus to which its manner of being and its fecundity assign one of the chief places among those with which the genius of mankind has enriched physics4 ,shortly afterwards1 our amateur would learn that ,carlisle and ,nicholson had decomposed water by the aid of a battery2 then1 that ,davy1 in #ahjc1 had produced1 by the help of the same battery1 a quite unexpected phenomenon1 and had succeeded in preparing metals endowed with marvellous properties1 beginning with substances of an earthy appearance which had been known for a long time1 but whose real nature had not been discovered4 ,in another order of ideas1 surprises as prodigious would wait for our amateur4 ,commencing with #ahjb1 he might have read the admirable series of memoirs which ,young then published1 and might thereby have learned how the study of the phenomena of diffraction led to the belief that the undulation theory1 which1 since the works of ,newton seemed irretrievably condemned1 was1 on the contrary1 beginning quite a new life4 ,a little later--in #ahjh--;he might have witnessed the discovery made by ,malus of polarization by reflexion1 and would have been able to note1 no doubt with stupefaction1 that under certain conditions a ray of light loses the property of being reflected4 ,he might also have heard of one ,rumford1 who was then promulgating very singular ideas on the nature of heat1 who thought that the then classical notions might be false1 that caloric does not exist as a fluid1 and who1 in #ahjd1 even demonstrated that heat is created by friction4 ,a few years later he would learn that ,charles had enunciated a capital law on the dilatation of gases2 that ,pierre ,prevost1 in #ahji1 was making a study1 full of original ideas1 on radiant heat4 ,in the meantime he would not have failed to read volumes iii4 and iv4 of the ,mecanique celeste of ,laplace1 published in #ahjd and #ahje1 and he might1 no doubt1 have thought that before long mathematics would enable physical science to develop with unforeseen safety4 ,all these results may doubtless be compared in importance with the present discoveries4 ,when strange metals like potassium and sodium were isolated by an entirely new method1 the astonishment must have been on a par with that caused in our time by the magnificent discovery of radium4 ,the polarization of light is a phenomenon as undoubtedly singular as the existence of the ,x rays2 and the upheaval produced in natural philosophy by the theories of the disintegration of matter and the ideas concerning electrons is probably not more considerable than that produced in the theories of light and heat by the works of ,young and ,rumford4 ,if we now disentangle ourselves from contingencies1 it will be understood that in reality physical science progresses by evolution rather than by revolution4 ,its march is continuous4 ,the facts which our theories enable us to discover1 subsist and are linked together long after these theories have disappeared4 ,out of the materials of former edifices overthrown1 new dwellings are constantly being reconstructed4 ,the labour of our forerunners never wholly perishes4 ,the ideas of yesterday prepare for those of to-morrow2 they contain them1 so to speak1 in potentia4 ,science is in some sort a living organism1 which gives birth to an indefinite series of new beings taking the places of the old1 and which evolves according to the nature of its environment1 adapting itself to external conditions1 and healing at every step the wounds which contact with reality may have occasioned4 ,sometimes this evolution is rapid1 sometimes it is slow enough2 but it obeys the ordinary laws4 ,the wants imposed by its surroundings create certain organs in science4 ,the problems set to physicists by the engineer who wishes to facilitate transport or to produce better illumination1 or by the doctor who seeks to know how such and such a remedy acts1 or1 again1 by the physiologist desirous of understanding the mechanism of the gaseous and liquid exchanges between the cell and the outer medium1 cause new chapters in physics to appear1 and suggest researches adapted to the necessities of actual life4 ,the evolution of the different parts of physics does not1 however1 take place with equal speed1 because the circumstances in which they are placed are not equally favourable4 ,sometimes a whole series of questions will appear forgotten1 and will live only with a languishing existence2 and then some accidental circumstance suddenly brings them new life1 and they become the object of manifold labours1 engross public attention1 and invade nearly the whole domain of science4 ,we have in our own day witnessed such a spectacle4 ,the discovery of the ,x rays--a discovery which physicists no doubt consider as the logical outcome of researches long pursued by a few scholars working in silence and obscurity on an otherwise much neglected subject-- seemed to the public eye to have inaugurated a new era in the history of physics4 ,if1 as is the case1 however1 the extraordinary scientific movement provoked by ,rntgen's sensational experiments has a very remote origin1 it has1 at least1 been singularly quickened by the favourable conditions created by the interest aroused in its astonishing applications to radiography4 ,a lucky chance has thus hastened an evolution already taking place1 and theories previously outlined have received a singular development4 ,without wishing to yield too much to what may be considered a whim of fashion1 we cannot1 if we are to note in this book the stage actually reached in the continuous march of physics1 refrain from giving a clearly preponderant place to the questions suggested by the study of the new radiations4 ,at the present time it is these questions which move us the most2 they have shown us unknown horizons1 and towards the fields recently opened to scientific activity the daily increasing crowd of searchers rushes in rather disorderly fashion4 ,one of the most interesting consequences of the recent discoveries has been to rehabilitate in the eyes of scholars1 speculations relating to the constitution of matter1 and1 in a more general way1 metaphysical problems4 ,philosophy has1 of course1 never been completely separated from science2 but in times past many physicists dissociated themselves from studies which they looked upon as unreal word-squabbles1 and sometimes not unreasonably abstained from joining in discussions which seemed to them idle and of rather puerile subtlety4 ,they had seen the ruin of most of the systems built up a priori by daring philosophers1 and deemed it more prudent to listen to the advice given by ,kirchhoff and to substitute the description of facts for a sham explanation of nature4 ,it should however be remarked that these physicists somewhat deceived themselves as to the value of their caution1 and that the mistrust they manifested towards philosophical speculations did not preclude their admitting1 unknown to themselves1 certain axioms which they did not discuss1 but which are1 properly speaking1 metaphysical conceptions4 ,they were unconsciously speaking a language taught them by their predecessors1 of which they made no attempt to discover the origin4 ,it is thus that it was readily considered evident that physics must necessarily some day re-enter the domain of mechanics1 and thence it was postulated that everything in nature is due to movement4 ,we1 further1 accepted the principles of the classical mechanics without discussing their legitimacy4 ,this state of mind was1 even of late years1 that of the most illustrious physicists4 ,it is manifested1 quite sincerely and without the slightest reserve1 in all the classical works devoted to physics4 ,thus ,verdet1 an illustrious professor who has had the greatest and most happy influence on the intellectual formation of a whole generation of scholars1 and whose works are even at the present day very often consulted1 wrote3 ,the true problem of the physicist is always to reduce all phenomena to that which seems to us the simplest and clearest1 that is to say1 to movement4 ,in his celebrated course of lectures at l'cole ,polytechnique1 ,jamin likewise said3 ,physics will one day form a chapter of general mechanics2 and in the preface to his excellent course of lectures on physics1 ,m4 ,violle1 in #ahhd1 thus expresses himself3 ,the science of nature tends towards mechanics by a necessary evolution1 the physicist being able to establish solid theories only on the laws of movement4 ,the same idea is again met with in the words of ,cornu in #ahif3 ,the general tendency should be to show how the facts observed and the phenomena measured1 though first brought together by empirical laws1 end1 by the impulse of successive progressions1 in coming under the general laws of rational mechanics2 and the same physicist showed clearly that in his mind this connexion of phenomena with mechanics had a deep and philosophical reason1 when1 in the fine discourse pronounced by him at the opening ceremony of the ,congrs de ,physique in #aijj1 he exclaimed3 ,the mind of ,descartes soars over modern physics1 or rather1 ,i should say1 he is their luminary4 ,the further we penetrate into the knowledge of natural phenomena1 the clearer and the more developed becomes the bold ,cartesian conception regarding the mechanism of the universe4 ,there is nothing in the physical world but matter and movement4 ,if we adopt this conception1 we are led to construct mechanical representations of the material world1 and to imagine movements in the different parts of bodies capable of reproducing all the manifestations of nature4 ,the kinematic knowledge of these movements1 that is to say1 the determination of the position1 speed1 and acceleration at a given moment of all the parts of the system1 or1 on the other hand1 their dynamical study1 enabling us to know what is the action of these parts on each other1 would then be sufficient to enable us to foretell all that can occur in the domain of nature4 ,this was the great thought clearly expressed by the ,encyclopdists of the eighteenth century2 and if the necessity of interpreting the phenomena of electricity or light led the physicists of last century to imagine particular fluids which seemed to obey with some difficulty the ordinary rules of mechanics1 these physicists still continued to retain their hope in the future1 and to treat the idea of ,descartes as an ideal to be reached sooner or later4 ,certain scholars--particularly those of the ,english ,school--outrunning experiment1 and pushing things to extremes1 took pleasure in proposing very curious mechanical models which were often strange images of reality4 ,the most illustrious of them1 ,lord ,kelvin1 may be considered as their representative type1 and he has himself said3 ,it seems to me that the true sense of the question1 ,do we or do we not understand a particular subject in physics8 is--,can we make a mechanical model which corresponds to it8 ,i am never satisfied so long as ,i have been unable to make a mechanical model of the object4 ,if ,i am able to do so1 ,i understand it4 ,if ,i cannot make such a model1 ,i do not understand it4 ,but it must be acknowledged that some of the models thus devised have become excessively complicated1 and this complication has for a long time discouraged all but very bold minds4 ,in addition1 when it became a question of penetrating into the mechanism of molecules1 and we were no longer satisfied to look at matter as a mass1 the mechanical solutions seemed undetermined and the stability of the edifices thus constructed was insufficiently demonstrated4 ,returning then to our starting-point1 many contemporary physicists wish to subject ,descartes' idea to strict criticism4 ,from the philosophical point of view1 they first enquire whether it is really demonstrated that there exists nothing else in the knowable than matter and movement4 ,they ask themselves whether it is not habit and tradition in particular which lead us to ascribe to mechanics the origin of phenomena4 ,perhaps also a question of sense here comes in4 ,our senses1 which are1 after all1 the only windows open towards external reality1 give us a view of one side of the world only2 evidently we only know the universe by the relations which exist between it and our organisms1 and these organisms are peculiarly sensitive to movement4 ,nothing1 however1 proves that those acquisitions which are the most ancient in historical order ought1 in the development of science1 to remain the basis of our knowledge4 ,nor does any theory prove that our perceptions are an exact indication of reality4 ,many reasons1 on the contrary1 might be invoked which tend to compel us to see in nature phenomena which cannot be reduced to movement4 ,mechanics as ordinarily understood is the study of reversible phenomena4 ,if there be given to the parameter which represents time1#a and which has assumed increasing values during the duration of the phenomena1 decreasing values which make it go the opposite way1 the whole system will again pass through exactly the same stages as before1 and all the phenomena will unfold themselves in reversed order4 ,in physics1 the contrary rule appears very general1 and reversibility generally does not exist4 ,it is an ideal and limited case1 which may be sometimes approached1 but can never1 strictly speaking1 be met with in its entirety4 ,no physical phenomenon ever recommences in an identical manner if its direction be altered4 ,it is true that certain mathematicians warn us that a mechanics can be devised in which reversibility would no longer be the rule1 but the bold attempts made in this direction are not wholly satisfactory4 ,footnote #a3 ,i4e41 the time-curve4--,,ed4 ,on the other hand1 it is established that if a mechanical explanation of a phenomenon can be given1 we can find an infinity of others which likewise account for all the peculiarities revealed by experiment4 ,but1 as a matter of fact1 no one has ever succeeded in giving an indisputable mechanical representation of the whole physical world4 ,even were we disposed to admit the strangest solutions of the problem2 to consent1 for example1 to be satisfied with the hidden systems devised by ,helmholtz1 whereby we ought to divide variable things into two classes1 some accessible1 and the others now and for ever unknown1 we should never manage to construct an edifice to contain all the known facts4 ,even the very comprehensive mechanics of a ,hertz fails where the classical mechanics has not succeeded4 ,deeming this check irremediable1 many contemporary physicists give up attempts which they look upon as condemned beforehand1 and adopt1 to guide them in their researches1 a method which at first sight appears much more modest1 and also much more sure4 ,they make up their minds not to see at once to the bottom of things2 they no longer seek to suddenly strip the last veils from nature1 and to divine her supreme secrets2 but they work prudently and advance but slowly1 while on the ground thus conquered foot by foot they endeavour to establish themselves firmly4 ,they study the various magnitudes directly accessible to their observation without busying themselves as to their essence4 ,they measure quantities of heat and of temperature1 differences of potential1 currents1 and magnetic fields2 and then1 varying the conditions1 apply the rules of experimental method1 and discover between these magnitudes mutual relations1 while they thus succeed in enunciating laws which translate and sum up their labours4 ,these empirical laws1 however1 themselves bring about by induction the promulgation of more general laws1 which are termed principles4 ,these principles are originally only the results of experiments1 and experiment allows them besides to be checked1 and their more or less high degree of generality to be verified4 ,when they have been thus definitely established1 they may serve as fresh starting-points1 and1 by deduction1 lead to very varied discoveries4 ,the principles which govern physical science are few in number1 and their very general form gives them a philosophical appearance1 while we cannot long resist the temptation of regarding them as metaphysical dogmas4 ,it thus happens that the least bold physicists1 those who have wanted to show themselves the most reserved1 are themselves led to forget the experimental character of the laws they have propounded1 and to see in them imperious beings whose authority1 placed above all verification1 can no longer be discussed4 ,others1 on the contrary1 carry prudence to the extent of timidity4 ,they desire to grievously limit the field of scientific investigation1 and they assign to science a too restricted domain4 ,they content themselves with representing phenomena by equations1 and think that they ought to submit to calculation magnitudes experimentally determined1 without asking themselves whether these calculations retain a physical meaning4 ,they are thus led to reconstruct a physics in which there again appears the idea of quality1 understood1 of course1 not in the scholastic sense1 since from this quality we can argue with some precision by representing it under numerical symbols1 but still constituting an element of differentiation and of heterogeneity4 ,notwithstanding the errors they may lead to if carried to excess1 both these doctrines render1 as a whole1 most important service4 ,it is no bad thing that these contradictory tendencies should subsist1 for this variety in the conception of phenomena gives to actual science a character of intense life and of veritable youth1 capable of impassioned efforts towards the truth4 ,spectators who see such moving and varied pictures passing before them1 experience the feeling that there no longer exist systems fixed in an immobility which seems that of death4 ,they feel that nothing is unchangeable2 that ceaseless transformations are taking place before their eyes2 and that this continuous evolution and perpetual change are the necessary conditions of progress4 ,a great number of seekers1 moreover1 show themselves on their own account perfectly eclectic4 ,they adopt1 according to their needs1 such or such a manner of looking at nature1 and do not hesitate to utilize very different images when they appear to them useful and convenient4 ,and1 without doubt1 they are not wrong1 since these images are only symbols convenient for language4 ,they allow facts to be grouped and associated1 but only present a fairly distant resemblance with the objective reality4 ,hence it is not forbidden to multiply and to modify them according to circumstances4 ,the really essential thing is to have1 as a guide through the unknown1 a map which certainly does not claim to represent all the aspects of nature1 but which1 having been drawn up according to predetermined rules1 allows us to follow an ascertained road in the eternal journey towards the truth4 ,among the provisional theories which are thus willingly constructed by scholars on their journey1 like edifices hastily run up to receive an unforeseen harvest1 some still appear very bold and very singular4 ,abandoning the search after mechanical models for all electrical phenomena1 certain physicists reverse1 so to speak1 the conditions of the problem1 and ask themselves whether1 instead of giving a mechanical interpretation to electricity1 they may not1 on the contrary1 give an electrical interpretation to the phenomena of matter and motion1 and thus merge mechanics itself in electricity4 ,one thus sees dawning afresh the eternal hope of co-ordinating all natural phenomena in one grandiose and imposing synthesis4 ,whatever may be the fate reserved for such attempts1 they deserve attention in the highest degree2 and it is desirable to examine them carefully if we wish to have an exact idea of the tendencies of modern physics4 ,,chapter ,,ii ,,measurements #a4 ,,metrology ,not so very long ago1 the scholar was often content with qualitative observations4 ,many phenomena were studied without much trouble being taken to obtain actual measurements4 ,but it is now becoming more and more understood that to establish the relations which exist between physical magnitudes1 and to represent the variations of these magnitudes by functions which allow us to use the power of mathematical analysis1 it is most necessary to express each magnitude by a definite number4 ,under these conditions alone can a magnitude be considered as effectively known4 ,i often say1 ,lord ,kelvin has said1 that if you can measure that of which you are speaking and express it by a number you know something of your subject2 but if you cannot measure it nor express it by a number1 your knowledge is of a sorry kind and hardly satisfactory4 ,it may be the beginning of the acquaintance1 but you are hardly1 in your thoughts1 advanced towards science1 whatever the subject may be4 ,it has now become possible to measure exactly the elements which enter into nearly all physical phenomena1 and these measurements are taken with ever increasing precision4 ,every time a chapter in science progresses1 science shows itself more exacting2 it perfects its means of investigation1 it demands more and more exactitude1 and one of the most striking features of modern physics is this constant care for strictness and clearness in experimentation4 ,a veritable science of measurement has thus been constituted which extends over all parts of the domain of physics4 ,this science has its rules and its methods2 it points out the best processes of calculation1 and teaches the method of correctly estimating errors and taking account of them4 ,it has perfected the processes of experiment1 co-ordinated a large number of results1 and made possible the unification of standards4 ,it is thanks to it that the system of measurements unanimously adopted by physicists has been formed4 ,at the present day we designate more peculiarly by the name of metrology that part of the science of measurements which devotes itself specially to the determining of the prototypes representing the fundamental units of dimension and mass1 and of the standards of the first order which are derived from them4 ,if all measurable quantities1 as was long thought possible1 could be reduced to the magnitudes of mechanics1 metrology would thus be occupied with the essential elements entering into all phenomena1 and might legitimately claim the highest rank in science4 ,but even when we suppose that some magnitudes can never be connected with mass1 length1 and time1 it still holds a preponderating place1 and its progress finds an echo throughout the whole domain of the natural sciences4 ,it is therefore well1 in order to give an account of the general progress of physics1 to examine at the outset the improvements which have been effected in these fundamental measurements1 and to see what precision these improvements have allowed us to attain4 #b4 ,,the ,,measure ,,of ,,length ,to measure a length is to compare it with another length taken as unity4 ,measurement is therefore a relative operation1 and can only enable us to know ratios4 ,did both the length to be measured and the unit chosen happen to vary simultaneously and in the same degree1 we should perceive no change4 ,moreover1 the unit being1 by definition1 the term of comparison1 and not being itself comparable with anything1 we have theoretically no means of ascertaining whether its length varies4 ,if1 however1 we were to note that1 suddenly and in the same proportions1 the distance between two points on this earth had increased1 that all the planets had moved further from each other1 that all objects around us had become larger1 that we ourselves had become taller1 and that the distance travelled by light in the duration of a vibration had become greater1 we should not hesitate to think ourselves the victims of an illusion1 that in reality all these distances had remained fixed1 and that all these appearances were due to a shortening of the rule which we had used as the standard for measuring the lengths4 ,from the mathematical point of view1 it may be considered that the two hypotheses are equivalent2 all has lengthened around us1 or else our standard has become less4 ,but it is no simple question of convenience and simplicity which leads us to reject the one supposition and to accept the other2 it is right in this case to listen to the voice of common sense1 and those physicists who have an instinctive trust in the notion of an absolute length are perhaps not wrong4 ,it is only by choosing our unit from those which at all times have seemed to all men the most invariable1 that we are able in our experiments to note that the same causes acting under identical conditions always produce the same effects4 ,the idea of absolute length is derived from the principle of causality2 and our choice is forced upon us by the necessity of obeying this principle1 which we cannot reject without declaring by that very act all science to be impossible4 ,similar remarks might be made with regard to the notions of absolute time and absolute movement4 ,they have been put in evidence and set forth very forcibly by a learned and profound mathematician1 ,m4 ,painlev4 ,on the particularly clear example of the measure of length1 it is interesting to follow the evolution of the methods employed1 and to run through the history of the progress in precision from the time that we have possessed authentic documents relating to this question4 ,this history has been written in a masterly way by one of the physicists who have in our days done the most by their personal labours to add to it glorious pages4 ,m4 ,benoit1 the learned ,director of the ,international ,bureau of ,weights and ,measures1 has furnished in various reports very complete details on the subject1 from which ,i here borrow the most interesting4 ,we know that in ,france the fundamental standard for measures of length was for a long time the ,toise du ,chtelet1 a kind of callipers formed of a bar of iron which in #affh was embedded in the outside wall of the ,chtelet1 at the foot of the staircase4 ,this bar had at its extremities two projections with square faces1 and all the toises of commerce had to fit exactly between them4 ,such a standard1 roughly constructed1 and exposed to all the injuries of weather and time1 offered very slight guarantees either as to the permanence or the correctness of its copies4 ,nothing1 perhaps1 can better convey an idea of the importance of the modifications made in the methods of experimental physics than the easy comparison between so rudimentary a process and the actual measurements effected at the present time4 ,the ,toise du ,chtelet1 notwithstanding its evident faults1 was employed for nearly a hundred years2 in #agff it was replaced by the ,toise du ,prou1 so called because it had served for the measurements of the terrestrial arc effected in ,peru from #agce to #agci by ,bouguer1 ,la ,condamine1 and ,godin4 ,at that time1 according to the comparisons made between this new toise and the ,toise du ,nord1 which had also been used for the measurement of an arc of the meridian1 an error of the tenth part of a millimetre in measuring lengths of the order of a metre was considered quite unimportant4 ,at the end of the eighteenth century1 ,delambre1 in his work ,sur la ,base du ,systme mtrique dcimal1 clearly gives us to understand that magnitudes of the order of the hundredth of a millimetre appear to him incapable of observation1 even in scientific researches of the highest precision4 ,at the present date the ,international ,bureau of ,weights and ,measures guarantees1 in the determination of a standard of length compared with the metre1 an approximation of two or three ten-thousandths of a millimetre1 and even a little more under certain circumstances4 ,this very remarkable progress is due to the improvements in the method of comparison on the one hand1 and in the manufacture of the standard on the other4 ,m4 ,benoit rightly points out that a kind of competition has been set up between the standard destined to represent the unit with its subdivisions and multiples and the instrument charged with observing it1 comparable1 up to a certain point1 with that which in another order of ideas goes on between the gun and the armour-plate4 ,the measuring instrument of to-day is an instrument of comparison constructed with meticulous care1 which enables us to do away with causes of error formerly ignored1 to eliminate the action of external phenomena1 and to withdraw the experiment from the influence of even the personality of the observer4 ,this standard is no longer1 as formerly1 a flat rule1 weak and fragile1 but a rigid bar1 incapable of deformation1 in which the material is utilised in the best conditions of resistance4 ,for a standard with ends has been substituted a standard with marks1 which permits much more precise definition and can be employed in optical processes of observation alone2 that is1 in processes which can produce in it no deformation and no alteration4 ,moreover1 the marks are traced on the plane of the neutral fibres#b exposed1 and the invariability of their distance apart is thus assured1 even when a change is made in the way the rule is supported4 ,footnote #b3 ,the author seems to refer to the fact that in the standard metre1 the measurement is taken from the central one of three marks at each end of the bar4 ,the transverse section of the bar is an ,x1 and the reading is made by a microscope4--,,ed4 ,thanks to studies thus systematically pursued1 we have succeeded in the course of a hundred years in increasing the precision of measures in the proportion of a thousand to one1 and we may ask ourselves whether such an increase will continue in the future4 ,no doubt progress will not be stayed2 but if we keep to the definition of length by a material standard1 it would seem that its precision cannot be considerably increased4 ,we have nearly reached the limit imposed by the necessity of making strokes of such a thickness as to be observable under the microscope4 ,it may happen1 however1 that we shall be brought one of these days to a new conception of the measure of length1 and that very different processes of determination will be thought of4 ,if we took as unit1 for instance1 the distance covered by a given radiation during a vibration1 the optical processes would at once admit of much greater precision4 ,thus ,fizeau1 the first to have this idea1 says3 ,a ray of light1 with its series of undulations of extreme tenuity but perfect regularity1 may be considered as a micrometer of the greatest perfection1 and particularly suitable for determining length4 ,but in the present state of things1 since the legal and customary definition of the unit remains a material standard1 it is not enough to measure length in terms of wave-lengths1 and we must also know the value of these wave-lengths in terms of the standard prototype of the metre4 ,this was determined in #ahid by ,m4 ,michelson and ,m4 ,benoit in an experiment which will remain classic4 ,the two physicists measured a standard length of about ten centimetres1 first in terms of the wave-lengths of the red1 green1 and blue radiations of cadmium1 and then in terms of the standard metre4 ,the great difficulty of the experiment proceeds from the vast difference which exists between the lengths to be compared1 the wave-lengths barely amounting to half a micron2#c the process employed consisted in noting1 instead of this length1 a length easily made about a thousand times greater1 namely1 the distance between the fringes of interference4 ,footnote #c3 ,i4e4 #a_/bjjj of a millimetre4--,,ed4 ,in all measurement1 that is to say in every determination of the relation of a magnitude to the unit1 there has to be determined on the one hand the whole1 and on the other the fractional part of this ratio1 and naturally the most delicate determination is generally that of this fractional part4 ,in optical processes the difficulty is reversed4 ,the fractional part is easily known1 while it is the high figure of the number representing the whole which becomes a very serious obstacle4 ,it is this obstacle which ,,mm4 ,michelson and ,benoit overcame with admirable ingenuity4 ,by making use of a somewhat similar idea1 ,m4 ,mac de ,lpinay and ,,mm4 ,perot and ,fabry1 have lately effected by optical methods1 measurements of the greatest precision1 and no doubt further progress may still be made4 ,a day may perhaps come when a material standard will be given up1 and it may perhaps even be recognised that such a standard in time changes its length by molecular strain1 and by wear and tear3 and it will be further noted that1 in accordance with certain theories which will be noticed later on1 it is not invariable when its orientation is changed4 ,for the moment1 however1 the need of any change in the definition of the unit is in no way felt2 we must1 on the contrary1 hope that the use of the unit adopted by the physicists of the whole world will spread more and more4 ,it is right to remark that a few errors still occur with regard to this unit1 and that these errors have been facilitated by incoherent legislation4 ,france herself1 though she was the admirable initiator of the metrical system1 has for too long allowed a very regrettable confusion to exist2 and it cannot be noted without a certain sadness that it was not until the #aath ,july #aijc that a law was promulgated re-establishing the agreement between the legal and the scientific definition of the metre4 ,perhaps it may not be useless to briefly indicate here the reasons of the disagreement which had taken place4 ,two definitions of the metre can be1 and in fact were given4 ,one had for its basis the dimensions of the earth1 the other the length of the material standard4 ,in the minds of the founders of the metrical system1 the first of these was the true definition of the unit of length1 the second merely a simple representation4 ,it was admitted1 however1 that this representation had been constructed in a manner perfect enough for it to be nearly impossible to perceive any difference between the unit and its representation1 and for the practical identity of the two definitions to be thus assured4 ,the creators of the metrical system were persuaded that the measurements of the meridian effected in their day could never be surpassed in precision2 and on the other hand1 by borrowing from nature a definite basis1 they thought to take from the definition of the unit some of its arbitrary character1 and to ensure the means of again finding the same unit if by any accident the standard became altered4 ,their confidence in the value of the processes they had seen employed was exaggerated1 and their mistrust of the future unjustified4 ,this example shows how imprudent it is to endeavour to fix limits to progress4 ,it is an error to think the march of science can be stayed2 and in reality it is now known that the ten-millionth part of the quarter of the terrestrial meridian is longer than the metre by #j4ahg millimetres4 ,but contemporary physicists do not fall into the same error as their forerunners1 and they regard the present result as merely provisional4 ,they guess1 in fact1 that new improvements will be effected in the art of measurement2 they know that geodesical processes1 though much improved in our days1 have still much to do to attain the precision displayed in the construction and determination of standards of the first order2 and consequently they do not propose to keep the ancient definition1 which would lead to having for unit a magnitude possessing the grave defect from a practical point of view of being constantly variable4 ,we may even consider that1 looked at theoretically1 its permanence would not be assured4 ,nothing1 in fact1 proves that sensible variations may not in time be produced in the value of an arc of the meridian1 and serious difficulties may arise regarding the probable inequality of the various meridians4 ,for all these reasons1 the idea of finding a natural unit has been gradually abandoned1 and we have become resigned to accepting as a fundamental unit an arbitrary and conventional length having a material representation recognised by universal consent2 and it was this unit which was consecrated by the following law of the #aath ,july #aijc3-- ,the standard prototype of the metrical system is the international metre1 which has been sanctioned by the ,general ,conference on ,weights and ,measures4 #c4 ,,the ,,measure ,,of ,,mass ,on the subject of measures of mass1 similar remarks to those on measures of length might be made4 ,the confusion here was perhaps still greater1 because1 to the uncertainty relating to the fixing of the unit1 was added some indecision on the very nature of the magnitude defined4 ,in law1 as in ordinary practice1 the notions of weight and of mass were not1 in fact1 separated with sufficient clearness4 ,they represent1 however1 two essentially different things4 ,mass is the characteristic of a quantity of matter2 it depends neither on the geographical position one occupies nor on the altitude to which one may rise2 it remains invariable so long as nothing material is added or taken away4 ,weight is the action which gravity has upon the body under consideration2 this action does not depend solely on the body1 but on the earth as well2 and when it is changed from one spot to another1 the weight changes1 because gravity varies with latitude and altitude4 ,these elementary notions1 to-day understood even by young beginners1 appear to have been for a long time indistinctly grasped4 ,the distinction remained confused in many minds1 because1 for the most part1 masses were comparatively estimated by the intermediary of weights4 ,the estimations of weight made with the balance utilize the action of the weight on the beam1 but in such conditions that the influence of the variations of gravity becomes eliminated4 ,the two weights which are being compared may both of them change if the weighing is effected in different places1 but they are attracted in the same proportion4 ,if once equal1 they remain equal even when in reality they may both have varied4 ,the current law defines the kilogramme as the standard of mass1 and the law is certainly in conformity with the rather obscurely expressed intentions of the founders of the metrical system4 ,their terminology was vague1 but they certainly had in view the supply of a standard for commercial transactions1 and it is quite evident that in barter what is important to the buyer as well as to the seller is not the attraction the earth may exercise on the goods1 but the quantity that may be supplied for a given price4 ,besides1 the fact that the founders abstained from indicating any specified spot in the definition of the kilogramme1 when they were perfectly acquainted with the considerable variations in the intensity of gravity1 leaves no doubt as to their real desire4 ,the same objections have been made to the definition of the kilogramme1 at first considered as the mass of a cubic decimetre of water at #d ,c41 as to the first definition of the metre4 ,we must admire the incredible precision attained at the outset by the physicists who made the initial determinations1 but we know at the present day that the kilogramme they constructed is slightly too heavy 7by about #a_/be1jjj74 ,very remarkable researches have been carried out with regard to this determination by the ,international ,bureau1 and by ,,mm4 ,mac de ,lpinay and ,buisson4 ,the law of the #aath ,july #aijc has definitely regularized the custom which physicists had adopted some years before2 and the standard of mass1 the legal prototype of the metrical system1 is now the international kilogramme sanctioned by the ,conference of ,weights and ,measures4 ,the comparison of a mass with the standard is effected with a precision to which no other measurement can attain4 ,metrology vouches for the hundredth of a milligramme in a kilogramme2 that is to say1 that it estimates the hundred-millionth part of the magnitude studied4 ,we may--as in the case of the lengths--ask ourselves whether this already admirable precision can be surpassed2 and progress would seem likely to be slow1 for difficulties singularly increase when we get to such small quantities4 ,but it is permitted to hope that the physicists of the future will do still better than those of to-day2 and perhaps we may catch a glimpse of the time when we shall begin to observe that the standard1 which is constructed from a heavy metal1 namely1 iridium-platinum1 itself obeys an apparently general law1 and little by little loses some particles of its mass by emanation4 #d4 ,,the ,,measure ,,of ,,time ,the third fundamental magnitude of mechanics is time4 ,there is1 so to speak1 no physical phenomenon in which the notion of time linked to the sequence of our states of consciousness does not play a considerable part4 ,ancestral habits and a very early tradition have led us to preserve1 as the unit of time1 a unit connected with the earth's movement2 and the unit to-day adopted is1 as we know1 the sexagesimal second of mean time4 ,this magnitude1 thus defined by the conditions of a natural motion which may itself be modified1 does not seem to offer all the guarantees desirable from the point of view of invariability4 ,it is certain that all the friction exercised on the earth--by the tides1 for instance--must slowly lengthen the duration of the day1 and must influence the movement of the earth round the sun4 ,such influence is certainly very slight1 but it nevertheless gives an unfortunately arbitrary character to the unit adopted4 ,we might have taken as the standard of time the duration of another natural phenomenon1 which appears to be always reproduced under identical conditions2 the duration1 for instance1 of a given luminous vibration4 ,but the experimental difficulties of evaluation with such a unit of the times which ordinarily have to be considered1 would be so great that such a reform in practice cannot be hoped for4 ,it should1 moreover1 be remarked that the duration of a vibration may itself be influenced by external circumstances1 among which are the variations of the magnetic field in which its source is placed4 ,it could not1 therefore1 be strictly considered as independent of the earth2 and the theoretical advantage which might be expected from this alteration would be somewhat illusory4 ,perhaps in the future recourse may be had to very different phenomena4 ,thus ,curie pointed out that if the air inside a glass tube has been rendered radioactive by a solution of radium1 the tube may be sealed up1 and it will then be noted that the radiation of its walls diminishes with time1 in accordance with an exponential law4 ,the constant of time derived by this phenomenon remains the same whatever the nature and dimensions of the walls of the tube or the temperature may be1 and time might thus be denned independently of all the other units4 ,we might also1 as ,m4 ,lippmann has suggested in an extremely ingenious way1 decide to obtain measures of time which can be considered as absolute because they are determined by parameters of another nature than that of the magnitude to be measured4 ,such experiments are made possible by the phenomena of gravitation4 ,we could employ1 for instance1 the pendulum by adopting1 as the unit of force1 the force which renders the constant of gravitation equal to unity4 ,the unit of time thus defined would be independent of the unit of length1 and would depend only on the substance which would give us the unit of mass under the unit of volume4 ,it would be equally possible to utilize electrical phenomena1 and one might devise experiments perfectly easy of execution4 ,thus1 by charging a condenser by means of a battery1 and discharging it a given number of times in a given interval of time1 so that the effect of the current of discharge should be the same as the effect of the output of the battery through a given resistance1 we could estimate1 by the measurement of the electrical magnitudes1 the duration of the interval noted4 ,a system of this kind must not be looked upon as a simple jeu d'esprit1 since this very practicable experiment would easily permit us to check1 with a precision which could be carried very far1 the constancy of an interval of time4 ,from the practical point of view1 chronometry has made in these last few years very sensible progress4 ,the errors in the movements of chronometers are corrected in a much more systematic way than formerly1 and certain inventions have enabled important improvements to be effected in the construction of these instruments4 ,thus the curious properties which steel combined with nickel--so admirably studied by ,m4,ch4,ed4 ,guillaume--exhibits in the matter of dilatation are now utilized so as to almost completely annihilate the influence of variations of temperature4 #e4 ,,the ,,measure ,,of ,,temperature ,from the three mechanical units we derive secondary units2 as1 for instance1 the unit of work or mechanical energy4 ,the kinetic theory takes temperature1 as well as heat itself1 to be a quantity of energy1 and thus seems to connect this notion with the magnitudes of mechanics4 ,but the legitimacy of this theory cannot be admitted1 and the calorific movement should also be a phenomenon so strictly confined in space that our most delicate means of investigation would not enable us to perceive it4 ,it is better1 then1 to continue to regard the unit of difference of temperature as a distinct unit1 to be added to the fundamental units4 ,to define the measure of a certain temperature1 we take1 in practice1 some arbitrary property of a body4 ,the only necessary condition of this property is1 that it should constantly vary in the same direction when the temperature rises1 and that it should possess1 at any temperature1 a well-marked value4 ,we measure this value by melting ice and by the vapour of boiling water under normal pressure1 and the successive hundredths of its variation1 beginning with the melting ice1 defines the percentage4 ,thermodynamics1 however1 has made it plain that we can set up a thermometric scale without relying upon any determined property of a real body4 ,such a scale has an absolute value independently of the properties of matter4 ,now it happens that if we make use for the estimation of temperatures1 of the phenomena of dilatation under a constant pressure1 or of the increase of pressure in a constant volume of a gaseous body1 we obtain a scale very near the absolute1 which almost coincides with it when the gas possesses certain qualities which make it nearly what is called a perfect gas4 ,this most lucky coincidence has decided the choice of the convention adopted by physicists4 ,they define normal temperature by means of the variations of pressure in a mass of hydrogen beginning with the initial pressure of a metre of mercury at #j ,c4 ,m4,p4 ,chappuis1 in some very precise experiments conducted with much method1 has proved that at ordinary temperatures the indications of such a thermometer are so close to the degrees of the theoretical scale that it is almost impossible to ascertain the value of the divergences1 or even the direction that they take4 ,the divergence becomes1 however1 manifest when we work with extreme temperatures4 ,it results from the useful researches of ,m4 ,daniel ,berthelot that we must subtract #j4ah from the indications of the hydrogen thermometer towards the temperature -#bdj ,c1 and add #j4je to #ajjj to equate them with the thermodynamic scale4 ,of course1 the difference would also become still more noticeable on getting nearer to the absolute zero2 for as hydrogen gets more and more cooled1 it gradually exhibits in a lesser degree the characteristics of a perfect gas4 ,to study the lower regions which border on that kind of pole of cold towards which are straining the efforts of the many physicists who have of late years succeeded in getting a few degrees further forward1 we may turn to a gas still more difficult to liquefy than hydrogen4 ,thus1 thermometers have been made of helium2 and from the temperature of -#bfj ,c4 downward the divergence of such a thermometer from one of hydrogen is very marked4 ,the measurement of very high temperatures is not open to the same theoretical objections as that of very low temperatures2 but1 from a practical point of view1 it is as difficult to effect with an ordinary gas thermometer4 ,it becomes impossible to guarantee the reservoir remaining sufficiently impermeable1 and all security disappears1 notwithstanding the use of recipients very superior to those of former times1 such as those lately devised by the physicists of the ,reichansalt4 ,this difficulty is obviated by using other methods1 such as the employment of thermo-electric couples1 such as the very convenient couple of ,m4 le ,chatelier2 but the graduation of these instruments can only be effected at the cost of a rather bold extrapolation4 ,m4,d4 ,berthelot has pointed out and experimented with a very interesting process1 founded on the measurement by the phenomena of interference of the refractive index of a column of air subjected to the temperature it is desired to measure4 ,it appears admissible that even at the highest temperatures the variation of the power of refraction is strictly proportional to that of the density1 for this proportion is exactly verified so long as it is possible to check it precisely4 ,we can thus1 by a method which offers the great advantage of being independent of the power and dimension of the envelopes employed--since the length of the column of air considered alone enters into the calculation--obtain results equivalent to those given by the ordinary air thermometer4 ,another method1 very old in principle1 has also lately acquired great importance4 ,for a long time we sought to estimate the temperature of a body by studying its radiation1 but we did not know any positive relation between this radiation and the temperature1 and we had no good experimental method of estimation1 but had recourse to purely empirical formulas and the use of apparatus of little precision4 ,now1 however1 many physicists1 continuing the classic researches of ,kirchhoff1 ,boltzmann1 ,professors ,wien and ,planck1 and taking their starting-point from the laws of thermodynamics1 have given formulas which establish the radiating power of a dark body as a function of the temperature and the wave-length1 or1 better still1 of the total power as a function of the temperature and wave-length corresponding to the maximum value of the power of radiation4 ,we see1 therefore1 the possibility of appealing for the measurement of temperature to a phenomenon which is no longer the variation of the elastic force of a gas1 and yet is also connected with the principles of thermodynamics4 ,this is what ,professors ,lummer and ,pringsheim have shown in a series of studies which may certainly be reckoned among the greatest experimental researches of the last few years4 ,they have constructed a radiator closely resembling the theoretically integral radiator which a closed isothermal vessel would be1 and with only a very small opening1 which allows us to collect from outside the radiations which are in equilibrium with the interior4 ,this vessel is formed of a hollow carbon cylinder1 heated by a current of high intensity2 the radiations are studied by means of a bolometer1 the disposition of which varies with the nature of the experiments4 ,it is hardly possible to enter into the details of the method1 but the result sufficiently indicates its importance4 ,it is now possible1 thanks to their researches1 to estimate a temperature of #bjjj ,c4 to within about #e4 ,ten years ago a similar approximation could hardly have been arrived at for a temperature of #ajjj ,c4 #f4 ,,derived ,,units ,,and ,,the ,,measure ,,of ,a ,,quantity ,,of ,,energy ,it must be understood that it is only by arbitrary convention that a dependency is established between a derived unit and the fundamental units4 ,the laws of numbers in physics are often only laws of proportion4 ,we transform them into laws of equation1 because we introduce numerical coefficients and choose the units on which they depend so as to simplify as much as possible the formulas most in use4 ,a particular speed1 for instance1 is in reality nothing else but a speed1 and it is only by the peculiar choice of unit that we can say that it is the space covered during the unit of time4 ,in the same way1 a quantity of electricity is a quantity of electricity2 and there is nothing to prove that1 in its essence1 it is really reducible to a function of mass1 of length1 and of time4 ,persons are still to be met with who seem to have some illusions on this point1 and who see in the doctrine of the dimensions of the units a doctrine of general physics1 while it is1 to say truth1 only a doctrine of metrology4 ,the knowledge of dimensions is valuable1 since it allows us1 for instance1 to easily verify the homogeneity of a formula1 but it can in no way give us any information on the actual nature of the quantity measured4 ,magnitudes to which we attribute like dimensions may be qualitatively irreducible one to the other4 ,thus the different forms of energy are measured by the same unit1 and yet it seems that some of them1 such as kinetic energy1 really depend on time2 while for others1 such as potential energy1 the dependency established by the system of measurement seems somewhat fictitious4 ,the numerical value of a quantity of energy of any nature should1 in the system ,c4,g4,s41 be expressed in terms of the unit called the erg2 but1 as a matter of fact1 when we wish to compare and measure different quantities of energy of varying forms1 such as electrical1 chemical1 and other quantities1 etc41 we nearly always employ a method by which all these energies are finally transformed and used to heat the water of a calorimeter4 ,it is therefore very important to study well the calorific phenomenon chosen as the unit of heat1 and to determine with precision its mechanical equivalent1 that is to say1 the number of ergs necessary to produce this unit4 ,this is a number which1 on the principle of equivalence1 depends neither on the method employed1 nor the time1 nor any other external circumstance4 ,as the result of the brilliant researches of ,rowland and of ,mr ,griffiths on the variations of the specific heat of water1 physicists have decided to take as calorific standard the quantity of heat necessary to raise a gramme of water from #ae to #af ,c41 the temperature being measured by the scale of the hydrogen thermometer of the ,international ,bureau4 ,on the other hand1 new determinations of the mechanical equivalent1 among which it is right to mention that of ,mr4 ,ames1 and a full discussion as to the best results1 have led to the adoption of the number #d4ahg to represent the number of ergs capable of producing the unit of heat4 ,in practice1 the measurement of a quantity of heat is very often effected by means of the ice calorimeter1 the use of which is particularly simple and convenient4 ,there is1 therefore1 a very special interest in knowing exactly the melting-point of ice4 ,m4 ,leduc1 who for several years has measured a great number of physical constants with minute precautions and a remarkable sense of precision1 concludes1 after a close discussion of the various results obtained1 that this heat is equal to #gi4a calories4 ,an error of almost a calorie had been committed by several renowned experimenters1 and it will be seen that in certain points the art of measurement may still be largely perfected4 ,to the unit of energy might be immediately attached other units4 ,for instance1 radiation being nothing but a flux of energy1 we could1 in order to establish photometric units1 divide the normal spectrum into bands of a given width1 and measure the power of each for the unit of radiating surface4 ,but1 notwithstanding some recent researches on this question1 we cannot yet consider the distribution of energy in the spectrum as perfectly known4 ,if we adopt the excellent habit which exists in some researches of expressing radiating energy in ergs1 it is still customary to bring the radiations to a standard giving1 by its constitution alone1 the unit of one particular radiation4 ,in particular1 the definitions are still adhered to which were adopted as the result of the researches of ,m4 ,violle on the radiation of fused platinum at the temperature of solidification2 and most physicists utilize in the ordinary methods of photometry the clearly defined notions of ,m4 ,blondel as to the luminous intensity of flux1 illumination 7clairement71 light 7clat71 and lighting 7clairage71 with the corresponding units1 decimal candle1 lumen1 lux1 carcel lamp1 candle per square centimetre1 and lumen-hour4#d ,footnote #d3 ,these are the magnitudes and units adopted at the ,international ,congress of ,electricians in #aijd4 ,for their definition and explanation1 see ,demanet1 ,notes de ,physique ,exprimentale 7,louvain1 #aije71 t4 iv4 p4 #h4--;,,ed4 #g4 ,,measure ,,of ,,certain ,,physical ,,constants ,the progress of metrology has led1 as a consequence1 to corresponding progress in nearly all physical measurements1 and particularly in the measure of natural constants4 ,among these1 the constant of gravitation occupies a position quite apart from the importance and simplicity of the physical law which defines it1 as well as by its generality4 ,two material particles are mutually attracted to each other by a force directly proportional to the product of their mass1 and inversely proportional to the square of the distance between them4 ,the coefficient of proportion is determined when once the units are chosen1 and as soon as we know the numerical values of this force1 of the two masses1 and of their distance4 ,but when we wish to make laboratory experiments serious difficulties appear1 owing to the weakness of the attraction between masses of ordinary dimensions4 ,microscopic forces1 so to speak1 have to be observed1 and therefore all the causes of errors have to be avoided which would be unimportant in most other physical researches4 ,it is known that ,cavendish was the first who succeeded by means of the torsion balance in effecting fairly precise measurements4 ,this method has been again taken in hand by different experimenters1 and the most recent results are due to ,mr ,vernon ,boys4 ,this learned physicist is also the author of a most useful practical invention1 and has succeeded in making quartz threads as fine as can be desired and extremely uniform4 ,he finds that these threads possess valuable properties1 such as perfect elasticity and great tenacity4 ,he has been able1 with threads not more than #a_/ejj of a millimetre in diameter1 to measure with precision couples of an order formerly considered outside the range of experiment1 and to reduce the dimensions of the apparatus of ,cavendish in the proportion of #aej to #a4 ,the great advantage found in the use of these small instruments is the better avoidance of the perturbations arising from draughts of air1 and of the very serious influence of the slightest inequality in temperature4 ,other methods have been employed in late years by other experimenters1 such as the method of ,baron ,etvs1 founded on the use of a torsion lever1 the method of the ordinary balance1 used especially by ,professors ,richarz and ,krigar-,menzel and also by ,professor ,poynting1 and the method of ,m4 ,wilsing1 who uses a balance with a vertical beam4 ,the results fairly agree1 and lead to attributing to the earth a density equal to #e4ebg4 ,the most familiar manifestation of gravitation is gravity4 ,the action of the earth on the unit of mass placed in one point1 and the intensity of gravity1 is measured1 as we know1 by the aid of a pendulum4 ,the methods of measurement1 whether by absolute or by relative determinations1 so greatly improved by ,borda and ,bessel1 have been still further improved by various geodesians1 among whom should be mentioned ,m4 von ,sterneek and ,general ,defforges4 ,numerous observations have been made in all parts of the world by various explorers1 and have led to a fairly complete knowledge of the distribution of gravity over the surface of the globe4 ,thus we have succeeded in making evident anomalies which would not easily find their place in the formula of ,clairaut4 ,another constant1 the determination of which is of the greatest utility in astronomy of position1 and the value of which enters into electromagnetic theory1 has to-day assumed1 with the new ideas on the constitution of matter1 a still more considerable importance4 ,i refer to the speed of light1 which appears to us1 as we shall see further on1 the maximum value of speed which can be given to a material body4 ,after the historical experiments of ,fizeau and ,foucault1 taken up afresh1 as we know1 partly by ,cornu1 and partly by ,michelson and ,newcomb1 it remained still possible to increase the precision of the measurements4 ,professor ,michelson has undertaken some new researches by a method which is a combination of the principle of the toothed wheel of ,fizeau with the revolving mirror of ,foucault4 ,the toothed wheel is here replaced1 however1 by a grating1 in which the lines and the spaces between them take the place of the teeth and the gaps1 the reflected light only being returned when it strikes on the space between two lines4 ,the illustrious ,american physicist estimates that he can thus evaluate to nearly five kilometres the path traversed by light in one second4 ,this approximation corresponds to a relative value of a few hundred-thousandths1 and it far exceeds those hitherto attained by the best experimenters4 ,when all the experiments are completed1 they will perhaps solve certain questions still in suspense2 for instance1 the question whether the speed of propagation depends on intensity4 ,if this turns out to be the case1 we should be brought to the important conclusion that the amplitude of the oscillations1 which is certainly very small in relation to the already tiny wave-lengths1 cannot be considered as unimportant in regard to these lengths4 ,such would seem to have been the result of the curious experiments of ,m4 ,muller and of ,m4 ,ebert1 but these results have been recently disputed by ,m4 ,doubt4 ,in the case of sound vibrations1 on the other hand1 it should be noted that experiment1 consistently with the theory1 proves that the speed increases with the amplitude1 or1 if you will1 with the intensity4 ,m4 ,violle has published an important series of experiments on the speed of propagation of very condensed waves1 on the deformations of these waves1 and on the relations of the speed and the pressure1 which verify in a remarkable manner the results foreshadowed by the already old calculations of ,riemann1 repeated later by ,hugoniot4 ,if1 on the contrary1 the amplitude is sufficiently small1 there exists a speed limit which is the same in a large pipe and in free air4 ,by some beautiful experiments1 ,,mm4 ,violle and ,vautier have clearly shown that any disturbance in the air melts somewhat quickly into a single wave of given form1 which is propagated to a distance1 while gradually becoming weaker and showing a constant speed which differs little in dry air at #j ,c4 from #cca4cf metres per second4 ,in a narrow pipe the influence of the walls makes itself felt and produces various effects1 in particular a kind of dispersion in space of the harmonics of the sound4 ,this phenomenon1 according to ,m4 ,brillouin1 is perfectly explicable by a theory similar to the theory of gratings4 ,,chapter ,,iii ,,principles #a4 ,,the ,,principles ,,of ,,physics ,facts conscientiously observed lead by induction to the enunciation of a certain number of laws or general hypotheses which are the principles already referred to4 ,these principal hypotheses are1 in the eyes of a physicist1 legitimate generalizations1 the consequences of which we shall be able at once to check by the experiments from which they issue4 ,among the principles almost universally adopted until lately figure prominently those of mechanics--such as the principle of relativity1 and the principle of the equality of action and reaction4 ,we will not detail nor discuss them here1 but later on we shall have an opportunity of pointing out how recent theories on the phenomena of electricity have shaken the confidence of physicists in them and have led certain scholars to doubt their absolute value4 ,the principle of ,lavoisier1 or principle of the conservation of mass1 presents itself under two different aspects according to whether mass is looked upon as the coefficient of the inertia of matter or as the factor which intervenes in the phenomena of universal attraction1 and particularly in gravitation4 ,we shall see when we treat of these theories1 how we have been led to suppose that inertia depended on velocity and even on direction4 ,if this conception were exact1 the principle of the invariability of mass would naturally be destroyed4 ,considered as a factor of attraction1 is mass really indestructible8 ,a few years ago such a question would have seemed singularly audacious4 ,and yet the law of ,lavoisier is so far from self-evident that for centuries it escaped the notice of physicists and chemists4 ,but its great apparent simplicity and its high character of generality1 when enunciated at the end of the eighteenth century1 rapidly gave it such an authority that no one was able to any longer dispute it unless he desired the reputation of an oddity inclined to paradoxical ideas4 ,it is important1 however1 to remark that1 under fallacious metaphysical appearances1 we are in reality using empty words when we repeat the aphorism1 ,nothing can be lost1 nothing can be created1 and deduce from it the indestructibility of matter4 ,this indestructibility1 in truth1 is an experimental fact1 and the principle depends on experiment4 ,it may even seem1 at first sight1 more singular than not that the weight of a bodily system in a given place1 or the quotient of this weight by that of the standard mass--that is to say1 the mass of these bodies--remains invariable1 both when the temperature changes and when chemical reagents cause the original materials to disappear and to be replaced by new ones4 ,we may certainly consider that in a chemical phenomenon annihilations and creations of matter are really produced2 but the experimental law teaches us that there is compensation in certain respects4 ,the discovery of the radioactive bodies has1 in some sort1 rendered popular the speculations of physicists on the phenomena of the disaggregation of matter4 ,we shall have to seek the exact meaning which ought to be given to the experiments on the emanation of these bodies1 and to discover whether these experiments really imperil the law of ,lavoisier4 ,for some years different experimenters have also effected many very precise measurements of the weight of divers bodies both before and after chemical reactions between these bodies4 ,two highly experienced and cautious physicists1 ,professors ,landolt and ,heydweiller1 have not hesitated to announce the sensational result that in certain circumstances the weight is no longer the same after as before the reaction4 ,in particular1 the weight of a solution of salts of copper in water is not the exact sum of the joint weights of the salt and the water4 ,such experiments are evidently very delicate2 they have been disputed1 and they cannot be considered as sufficient for conviction4 ,it follows nevertheless that it is no longer forbidden to regard the law of ,lavoisier as only an approximate law2 according to ,sandford and ,ray1 this approximation would be about #a_/b1djj1jjj4 ,this is also the result reached by ,professor ,poynting in experiments regarding the possible action of temperature on the weight of a body2 and if this be really so1 we may reassure ourselves1 and from the point of view of practical application may continue to look upon matter as indestructible4 ,the principles of physics1 by imposing certain conditions on phenomena1 limit after a fashion the field of the possible4 ,among these principles is one which1 notwithstanding its importance when compared with that of universally known principles1 is less familiar to some people4 ,this is the principle of symmetry1 more or less conscious applications of which can1 no doubt1 be found in various works and even in the conceptions of ,copernican astronomers1 but which was generalized and clearly enunciated for the first time by the late ,m4 ,curie4 ,this illustrious physicist pointed out the advantage of introducing into the study of physical phenomena the considerations on symmetry familiar to crystallographers2 for a phenomenon to take place1 it is necessary that a certain dissymmetry should previously exist in the medium in which this phenomenon occurs4 ,a body1 for instance1 may be animated with a certain linear velocity or a speed of rotation2 it may be compressed1 or twisted2 it may be placed in an electric or in a magnetic field2 it may be affected by an electric current or by one of heat2 it may be traversed by a ray of light either ordinary or polarized rectilineally or circularly1 etc43--in each case a certain minimum and characteristic dissymmetry is necessary at every point of the body in question4 ,this consideration enables us to foresee that certain phenomena which might be imagined a priori cannot exist4 ,thus1 for instance1 it is impossible that an electric field1 a magnitude directed and not superposable on its image in a mirror perpendicular to its direction1 could be created at right angles to the plane of symmetry of the medium2 while it would be possible to create a magnetic field under the same conditions4 ,this consideration thus leads us to the discovery of new phenomena2 but it must be understood that it cannot of itself give us absolutely precise notions as to the nature of these phenomena1 nor disclose their order of magnitude4 #b4 ,,the ,,principle ,,of ,,the ,,conservation ,,of ,,energy ,dominating not physics alone1 but nearly every other science1 the principle of the conservation of energy is justly considered as the grandest conquest of contemporary thought4 ,it shows us in a powerful light the most diverse questions2 it introduces order into the most varied studies2 it leads to a clear and coherent interpretation of phenomena which1 without it1 appear to have no connexion with each other2 and it supplies precise and exact numerical relations between the magnitudes which enter into these phenomena4 ,the boldest minds have an instinctive confidence in it1 and it is the principle which has most stoutly resisted that assault which the daring of a few theorists has lately directed to the overthrow of the general principles of physics4 ,at every new discovery1 the first thought of physicists is to find out how it accords with the principle of the conservation of energy4 ,the application of the principle1 moreover1 never fails to give valuable hints on the new phenomenon1 and often even suggests a complementary discovery4 ,up till now it seems never to have received a check1 even the extraordinary properties of radium not seriously contradicting it2 also the general form in which it is enunciated gives it such a suppleness that it is no doubt very difficult to overthrow4 ,i do not claim to set forth here the complete history of this principle1 but ,i will endeavour to show with what pains it was born1 how it was kept back in its early days and then obstructed in its development by the unfavourable conditions of the surroundings in which it appeared4 ,it first of all came1 in fact1 to oppose itself to the reigning theories2 but1 little by little1 it acted on these theories1 and they were modified under its pressure2 then1 in their turn1 these theories reacted on it and changed its primitive form4 ,it had to be made less wide in order to fit into the classic frame1 and was absorbed by mechanics2 and if it thus became less general1 it gained in precision what it lost in extent4 ,when once definitely admitted and classed1 as it were1 in the official domain of science1 it endeavoured to burst its bonds and return to a more independent and larger life4 ,the history of this principle is similar to that of all evolutions4 ,it is well known that the conservation of energy was1 at first1 regarded from the point of view of the reciprocal transformations between heat and work1 and that the principle received its first clear enunciation in the particular case of the principle of equivalence4 ,it is1 therefore1 rightly considered that the scholars who were the first to doubt the material nature of caloric were the precursors of ,r4 ,mayer2 their ideas1 however1 were the same as those of the celebrated ,german doctor1 for they sought especially to demonstrate that heat was a mode of motion4 ,without going back to early and isolated attempts like those of ,daniel ,bernoulli1 who1 in his hydrodynamics1 propounded the basis of the kinetic theory of gases1 or the researches of ,boyle on friction1 we may recall1 to show how it was propounded in former times1 a rather forgotten page of the ,mmoire sur la ,chaleur1 published in #aghj by ,lavoisier and ,laplace3 ,other physicists1 they wrote1 after setting out the theory of caloric1 think that heat is nothing but the result of the insensible vibrations of matter4444 ,in the system we are now examining1 heat is the vis viva resulting from the insensible movements of the molecules of a body2 it is the sum of the products of the mass of each molecule by the square of its velocity4444 ,we shall not decide between the two preceding hypotheses2 several phenomena seem to support the last mentioned--for instance1 that of the heat produced by the friction of two solid bodies4 ,but there are others which are more simply explained by the first1 and perhaps they both operate at once4 ,most of the physicists of that period1 however1 did not share the prudent doubts of ,lavoisier and ,laplace4 ,they admitted1 without hesitation1 the first hypothesis2 and1 four years after the appearance of the ,mmoire sur la ,chaleur1 ,sigaud de ,lafond1 a professor of physics of great reputation1 wrote3 ,pure ,fire1 free from all state of combination1 seems to be an assembly of particles of a simple1 homogeneous1 and absolutely unalterable matter1 and all the properties of this element indicate that these particles are infinitely small and free1 that they have no sensible cohesion1 and that they are moved in every possible direction by a continual and rapid motion which is essential to them4444 ,the extreme tenacity and the surprising mobility of its molecules are manifestly shown by the ease with which it penetrates into the most compact bodies and by its tendency to put itself in equilibrium throughout all bodies near to it4 ,it must be acknowledged1 however1 that the idea of ,lavoisier and ,laplace was rather vague and even inexact on one important point4 ,they admitted it to be evident that all variations of heat1 whether real or apparent1 undergone by a bodily system when changing its state1 are produced in inverse order when the system passes back to its original state4 ,this phrase is the very denial of equivalence where these changes of state are accompanied by external work4 ,laplace1 moreover1 himself became later a very convinced partisan of the hypothesis of the material nature of caloric1 and his immense authority1 so fortunate in other respects for the development of science1 was certainly in this case the cause of the retardation of progress4 ,the names of ,young1 ,rumford1 ,davy1 are often quoted among those physicists who1 at the commencement of the nineteenth century1 caught sight of the new truths as to the nature of heat4 ,to these names is very properly added that of ,sadi ,carnot4 ,a note found among his papers unquestionably proves that1 before #ahcj1 ideas had occurred to him from which it resulted that in producing work an equivalent amount of heat was destroyed4 ,but the year #ahdb is particularly memorable in the history of science as the year in which ,jules ,robert ,mayer succeeded1 by an entirely personal effort1 in really enunciating the principle of the conservation of energy4 ,chemists recall with just pride that the ,remarques sur les forces de la nature anime1 contemptuously rejected by all the journals of physics1 were received and published in the ,annalen of ,liebig4 ,we ought never to forget this example1 which shows with what difficulty a new idea contrary to the classic theories of the period succeeds in coming to the front2 but extenuating circumstances may be urged on behalf of the physicists4 ,robert ,mayer had a rather insufficient mathematical education1 and his ,memoirs1 the ,remarques1 as well as the ulterior publications1 ,mmoire sur le mouvement organique et la nutrition and the ,matriaux pour la dynamique du ciel1 contain1 side by side with very profound ideas1 evident errors in mechanics4 ,thus it often happens that discoveries put forward in a somewhat vague manner by adventurous minds not overburdened by the heavy baggage of scientific erudition1 who audaciously press forward in advance of their time1 fall into quite intelligible oblivion until rediscovered1 clarified1 and put into shape by slower but surer seekers4 ,this was the case with the ideas of ,mayer4 ,they were not understood at first sight1 not only on account of their originality1 but also because they were couched in incorrect language4 ,mayer was1 however1 endowed with a singular strength of thought2 he expressed in a rather confused manner a principle which1 for him1 had a generality greater than mechanics itself1 and so his discovery was in advance not only of his own time but of half the century4 ,he may justly be considered the founder of modern energetics4 ,freed from the obscurities which prevented its being clearly perceived1 his idea stands out to-day in all its imposing simplicity4 ,yet it must be acknowledged that if it was somewhat denaturalised by those who endeavoured to adapt it to the theories of mechanics1 and if it at first lost its sublime stamp of generality1 it thus became firmly fixed and consolidated on a more stable basis4 ,the efforts of ,helmholtz1 ,clausius1 and ,lord ,kelvin to introduce the principle of the conservation of energy into mechanics1 were far from useless4 ,these illustrious physicists succeeded in giving a more precise form to its numerous applications2 and their attempts thus contributed1 by reaction1 to give a fresh impulse to mechanics1 and allowed it to be linked to a more general order of facts4 ,if energetics has not been able to be included in mechanics1 it seems indeed that the attempt to include mechanics in energetics was not in vain4 ,in the middle of the last century1 the explanation of all natural phenomena seemed more and more referable to the case of central forces4 ,everywhere it was thought that reciprocal actions between material points could be perceived1 these points being attracted or repelled by each other with an intensity depending only on their distance or their mass4 ,if1 to a system thus composed1 the laws of the classical mechanics are applied1 it is shown that half the sum of the product of the masses by the square of the velocities1 to which is added the work which might be accomplished by the forces to which the system would be subject if it returned from its actual to its initial position1 is a sum constant in quantity4 ,this sum1 which is the mechanical energy of the system1 is therefore an invariable quantity in all the states to which it may be brought by the interaction of its various parts1 and the word energy well expresses a capital property of this quantity4 ,for if two systems are connected in such a way that any change produced in the one necessarily brings about a change in the other1 there can be no variation in the characteristic quantity of the second except so far as the characteristic quantity of the first itself varies--on condition1 of course1 that the connexions are made in such a manner as to introduce no new force4 ,it will thus be seen that this quantity well expresses the capacity possessed by a system for modifying the state of a neighbouring system to which we may suppose it connected4 ,now this theorem of pure mechanics was found wanting every time friction took place--that is to say1 in all really observable cases4 ,the more perceptible the friction1 the more considerable the difference2 but1 in addition1 a new phenomenon always appeared and heat was produced4 ,by experiments which are now classic1 it became established that the quantity of heat thus created independently of the nature of the bodies is always 7provided no other phenomena intervene7 proportional to the energy which has disappeared4 ,reciprocally1 also1 heat may disappear1 and we always find a constant relation between the quantities of heat and work which mutually replace each other4 ,it is quite clear that such experiments do not prove that heat is work4 ,we might just as well say that work is heat4 ,it is making a gratuitous hypothesis to admit this reduction of heat to mechanism2 but this hypothesis was so seductive1 and so much in conformity with the desire of nearly all physicists to arrive at some sort of unity in nature1 that they made it with eagerness and became unreservedly convinced that heat was an active internal force4 ,their error was not in admitting this hypothesis2 it was a legitimate one since it has proved very fruitful4 ,but some of them committed the fault of forgetting that it was an hypothesis1 and considered it a demonstrated truth4 ,moreover1 they were thus brought to see in phenomena nothing but these two particular forms of energy which in their minds were easily identified with each other4 ,from the outset1 however1 it became manifest that the principle is applicable to cases where heat plays only a parasitical part4 ,there were thus discovered1 by translating the principle of equivalence1 numerical relations between the magnitudes of electricity1 for instance1 and the magnitudes of mechanics4 ,heat was a sort of variable intermediary convenient for calculation1 but introduced in a roundabout way and destined to disappear in the final result4 ,verdet1 who1 in lectures which have rightly remained celebrated1 defined with remarkable clearness the new theories1 said1 in #ahfb3 ,electrical phenomena are always accompanied by calorific manifestations1 of which the study belongs to the mechanical theory of heat4 ,this study1 moreover1 will not only have the effect of making known to us interesting facts in electricity1 but will throw some light on the phenomena of electricity themselves4 ,the eminent professor was thus expressing the general opinion of his contemporaries1 but he certainly seemed to have felt in advance that the new theory was about to penetrate more deeply into the inmost nature of things4 ,three years previously1 ,rankine also had put forth some very remarkable ideas the full meaning of which was not at first well understood4 ,he it was who comprehended the utility of employing a more inclusive term1 and invented the phrase energetics4 ,he also endeavoured to create a new doctrine of which rational mechanics should be only a particular case2 and he showed that it was possible to abandon the ideas of atoms and central forces1 and to construct a more general system by substituting for the ordinary consideration of forces that of the energy which exists in all bodies1 partly in an actual1 partly in a potential state4 ,by giving more precision to the conceptions of ,rankine1 the physicists of the end of the nineteenth century were brought to consider that in all physical phenomena there occur apparitions and disappearances which are balanced by various energies4 ,it is natural1 however1 to suppose that these equivalent apparitions and disappearances correspond to transformations and not to simultaneous creations and destructions4 ,we thus represent energy to ourselves as taking different forms--mechanical1 electrical1 calorific1 and chemical-- capable of changing one into the other1 but in such a way that the quantitative value always remains the same4 ,in like manner a bank draft may be represented by notes1 gold1 silver1 or bullion4 ,the earliest known form of energy1 i4e4 work1 will serve as the standard as gold serves as the monetary standard1 and energy in all its forms will be estimated by the corresponding work4 ,in each particular case we can strictly define and measure1 by the correct application of the principle of the conservation of energy1 the quantity of energy evolved under a given form4 ,we can thus arrange a machine comprising a body capable of evolving this energy2 then we can force all the organs of this machine to complete an entirely closed cycle1 with the exception of the body itself1 which1 however1 has to return to such a state that all the variables from which this state depends resume their initial values except the particular variable to which the evolution of the energy under consideration is linked4 ,the difference between the work thus accomplished and that which would have been obtained if this variable also had returned to its original value1 is the measure of the energy evolved4 ,in the same way that1 in the minds of mechanicians1 all forces of whatever origin1 which are capable of compounding with each other and of balancing each other1 belong to the same category of beings1 so for many physicists energy is a sort of entity which we find under various aspects4 ,there thus exists for them a world1 which comes in some way to superpose itself upon the world of matter--that is to say1 the world of energy1 dominated in its turn by a fundamental law similar to that of ,lavoisier4#e ,this conception1 as we have already seen1 passes the limit of experience2 but others go further still4 ,absorbed in the contemplation of this new world1 they succeed in persuading themselves that the old world of matter has no real existence and that energy is sufficient by itself to give us a complete comprehension of the ,universe and of all the phenomena produced in it4 ,they point out that all our sensations correspond to changes of energy1 and that everything apparent to our senses is1 in truth1 energy4 ,the famous experiment of the blows with a stick by which it was demonstrated to a sceptical philosopher that an outer world existed1 only proves1 in reality1 the existence of energy1 and not that of matter4 ,the stick in itself is inoffensive1 as ,professor ,ostwald remarks1 and it is its vis viva1 its kinetic energy1 which is painful to us2 while if we possessed a speed equal to its own1 moving in the same direction1 it would no longer exist so far as our sense of touch is concerned4 ,footnote #e3 ,nothing is created2 nothing is lost--,,ed4 ,on this hypothesis1 matter would only be the capacity for kinetic energy1 its pretended impenetrability energy of volume1 and its weight energy of position in the particular form which presents itself in universal gravitation2 nay1 space itself would only be known to us by the expenditure of energy necessary to penetrate it4 ,thus in all physical phenomena we should only have to regard the quantities of energy brought into play1 and all the equations which link the phenomena to one another would have no meaning but when they apply to exchanges of energy4 ,for energy alone can be common to all phenomena4 ,this extreme manner of regarding things is seductive by its originality1 but appears somewhat insufficient if1 after enunciating generalities1 we look more closely into the question4 ,from the philosophical point of view it may1 moreover1 seem difficult not to conclude1 from the qualities which reveal1 if you will1 the varied forms of energy1 that there exists a substance possessing these qualities4 ,this energy1 which resides in one region1 and which transports itself from one spot to another1 forcibly brings to mind1 whatever view we may take of it1 the idea of matter4 ,helmholtz endeavoured to construct a mechanics based on the idea of energy and its conservation1 but he had to invoke a second law1 the principle of least action4 ,if he thus succeeded in dispensing with the hypothesis of atoms1 and in showing that the new mechanics gave us to understand the impossibility of certain movements which1 according to the old1 ought to have been but never were experimentally produced1 he was only able to do so because the principle of least action necessary for his theory became evident in the case of those irreversible phenomena which alone really exist in ,nature4 ,the energetists have thus not succeeded in forming a thoroughly sound system1 but their efforts have at all events been partly successful4 ,most physicists are of their opinion1 that kinetic energy is only a particular variety of energy to which we have no right to wish to connect all its other forms4 ,if these forms showed themselves to be innumerable throughout the ,universe1 the principle of the conservation of energy would1 in fact1 lose a great part of its importance4 ,every time that a certain quantity of energy seemed to appear or disappear1 it would always be permissible to suppose that an equivalent quantity had appeared or disappeared somewhere else under a new form2 and thus the principle would in a way vanish4 ,but the known forms of energy are fairly restricted in number1 and the necessity of recognising new ones seldom makes itself felt4 ,we shall see1 however1 that to explain1 for instance1 the paradoxical properties of radium and to re-establish concord between these properties and the principle of the conservation of energy1 certain physicists have recourse to the hypothesis that radium borrows an unknown energy from the medium in which it is plunged4 ,this hypothesis1 however1 is in no way necessary2 and in a few other rare cases in which similar hypotheses have had to be set up1 experiment has always in the long run enabled us to discover some phenomenon which had escaped the first observers and which corresponds exactly to the variation of energy first made evident4 ,one difficulty1 however1 arises from the fact that the principle ought only to be applied to an isolated system4 ,whether we imagine actions at a distance or believe in intermediate media1 we must always recognise that there exist no bodies in the world incapable of acting on each other1 and we can never affirm that some modification in the energy of a given place may not have its echo in some unknown spot afar off4 ,this difficulty may sometimes render the value of the principle rather illusory4 ,similarly1 it behoves us not to receive without a certain distrust the extension by certain philosophers to the whole ,universe1 of a property demonstrated for those restricted systems which observation can alone reach4 ,we know nothing of the ,universe as a whole1 and every generalization of this kind outruns in a singular fashion the limit of experiment4 ,even reduced to the most modest proportions1 the principle of the conservation of energy retains1 nevertheless1 a paramount importance2 and it still preserves1 if you will1 a high philosophical value4 ,m4,j4 ,perrin justly points out that it gives us a form under which we are experimentally able to grasp causality1 and that it teaches us that a result has to be purchased at the cost of a determined effort4 ,we can1 in fact1 with ,m4 ,perrin and ,m4 ,langevin1 represent this in a way which puts this characteristic in evidence by enunciating it as follows3 ,if at the cost of a change ,c we can obtain a change ,k1 there will never be acquired at the same cost1 whatever the mechanism employed1 first the change ,k and in addition some other change1 unless this latter be one that is otherwise known to cost nothing to produce or to destroy4 ,if1 for instance1 the fall of a weight can be accompanied1 without anything else being produced1 by another transformation--the melting of a certain mass of ice1 for example--it will be impossible1 no matter how you set about it or whatever the mechanism used1 to associate this same transformation with the melting of another weight of ice4 ,we can thus1 in the transformation in question1 obtain an appropriate number which will sum up that which may be expected from the external effect1 and can give1 so to speak1 the price at which this transformation is bought1 measure its invariable value by a common measure 7for instance1 the melting of the ice71 and1 without any ambiguity1 define the energy lost during the transformation as proportional to the mass of ice which can be associated with it4 ,this measure is1 moreover1 independent of the particular phenomenon taken as the common measure4 #c4 ,,the ,,principle ,,of ,,carnot ,,and ,,clausius ,the principle of ,carnot1 of a nature analogous to the principle of the conservation of energy1 has also a similar origin4 ,it was first enunciated1 like the last named1 although prior to it in time1 in consequence of considerations which deal only with heat and mechanical work4 ,like it1 too1 it has evolved1 grown1 and invaded the entire domain of physics4 ,it may be interesting to examine rapidly the various phases of this evolution4 ,the origin of the principle of ,carnot is clearly determined1 and it is very rare to be able to go back thus certainly to the source of a discovery4 ,sadi ,carnot had1 truth to say1 no precursor4 ,in his time heat engines were not yet very common1 and no one had reflected much on their theory4 ,he was doubtless the first to propound to himself certain questions1 and certainly the first to solve them4 ,it is known how1 in #ahbd1 in his ,rflexions sur la puissance motrice du feu1 he endeavoured to prove that the motive power of heat is independent of the agents brought into play for its realization1 and that its quantity is fixed solely by the temperature of the bodies between which1 in the last resort1 the transport of caloric is effected--at least in all engines in which the method of developing the motive power attains the perfection of which it is capable2 and this is1 almost textually1 one of the enunciations of the principle at the present day4 ,carnot perceived very clearly the great fact that1 to produce work by heat1 it is necessary to have at one's disposal a fall of temperature4 ,on this point he expresses himself with perfect clearness3 ,the motive power of a fall of water depends on its height and on the quantity of liquid2 the motive power of heat depends also on the quantity of caloric employed1 and on what might be called--in fact1 what we shall call--the height of fall1 that is to say1 the difference in temperature of the bodies between which the exchange of caloric takes place4 ,starting with this idea1 he endeavours to demonstrate1 by associating two engines capable of working in a reversible cycle1 that the principle is founded on the impossibility of perpetual motion4 ,his memoir1 now celebrated1 did not produce any great sensation1 and it had almost fallen into deep oblivion1 which1 in consequence of the discovery of the principle of equivalence1 might have seemed perfectly justified4 ,written1 in fact1 on the hypothesis of the indestructibility of caloric1 it was to be expected that this memoir should be condemned in the name of the new doctrine1 that is1 of the principle recently brought to light4 ,it was really making a new discovery to establish that ,carnot's fundamental idea survived the destruction of the hypothesis on the nature of heat1 on which he seemed to rely4 ,as he no doubt himself perceived1 his idea was quite independent of this hypothesis1 since1 as we have seen1 he was led to surmise that heat could disappear2 but his demonstrations needed to be recast and1 in some points1 modified4 ,it is to ,clausius that was reserved the credit of rediscovering the principle1 and of enunciating it in language conformable to the new doctrines1 while giving it a much greater generality4 ,the postulate arrived at by experimental induction1 and which must be admitted without demonstration1 is1 according to ,clausius1 that in a series of transformations in which the final is identical with the initial stage1 it is impossible for heat to pass from a colder to a warmer body unless some other accessory phenomenon occurs at the same time4 ,still more correctly1 perhaps1 an enunciation can be given of the postulate which1 in the main1 is analogous1 by saying3 ,a heat motor1 which after a series of transformations returns to its initial state1 can only furnish work if there exist at least two sources of heat1 and if a certain quantity of heat is given to one of the sources1 which can never be the hotter of the two4 ,by the expression source of heat1 we mean a body exterior to the system and capable of furnishing or withdrawing heat from it4 ,starting with this principle1 we arrive1 as does ,clausius1 at the demonstration that the output of a reversible machine working between two given temperatures is greater than that of any non-reversible engine1 and that it is the same for all reversible machines working between these two temperatures4 ,this is the very proposition of ,carnot2 but the proposition thus stated1 while very useful for the theory of engines1 does not yet present any very general interest4 ,clausius1 however1 drew from it much more important consequences4 ,first1 he showed that the principle conduces to the definition of an absolute scale of temperature2 and then he was brought face to face with a new notion which allows a strong light to be thrown on the questions of physical equilibrium4 ,i refer to entropy4 ,it is still rather difficult to strip entirely this very important notion of all analytical adornment4 ,many physicists hesitate to utilize it1 and even look upon it with some distrust1 because they see in it a purely mathematical function without any definite physical meaning4 ,perhaps they are here unduly severe1 since they often admit too easily the objective existence of quantities which they cannot define4 ,thus1 for instance1 it is usual almost every day to speak of the heat possessed by a body4 ,yet no body in reality possesses a definite quantity of heat even relatively to any initial state2 since starting from this point of departure1 the quantities of heat it may have gained or lost vary with the road taken and even with the means employed to follow it4 ,these expressions of heat gained or lost are1 moreover1 themselves evidently incorrect1 for heat can no longer be considered as a sort of fluid passing from one body to another4 ,the real reason which makes entropy somewhat mysterious is that this magnitude does not fall directly under the ken of any of our senses2 but it possesses the true characteristic of a concrete physical magnitude1 since it is1 in principle at least1 measurable4 ,various authors of thermodynamical researches1 amongst whom ,m4 ,mouret should be particularly mentioned1 have endeavoured to place this characteristic in evidence4 ,consider an isothermal transformation4 ,instead of leaving the heat abandoned by the body subjected to the transformation--water condensing in a state of saturated vapour1 for instance--to pass directly into an ice calorimeter1 we can transmit this heat to the calorimeter by the intermediary of a reversible ,carnot engine4 ,the engine having absorbed this quantity of heat1 will only give back to the ice a lesser quantity of heat2 and the weight of the melted ice1 inferior to that which might have been directly given back1 will serve as a measure of the isothermal transformation thus effected4 ,it can be easily shown that this measure is independent of the apparatus used4 ,it consequently becomes a numerical element characteristic of the body considered1 and is called its entropy4 ,entropy1 thus defined1 is a variable which1 like pressure or volume1 might serve concurrently with another variable1 such as pressure or volume1 to define the state of a body4 ,it must be perfectly understood that this variable can change in an independent manner1 and that it is1 for instance1 distinct from the change of temperature4 ,it is also distinct from the change which consists in losses or gains of heat4 ,in chemical reactions1 for example1 the entropy increases without the substances borrowing any heat4 ,when a perfect gas dilates in a vacuum its entropy increases1 and yet the temperature does not change1 and the gas has neither been able to give nor receive heat4 ,we thus come to conceive that a physical phenomenon cannot be considered known to us if the variation of entropy is not given1 as are the variations of temperature and of pressure or the exchanges of heat4 ,the change of entropy is1 properly speaking1 the most characteristic fact of a thermal change4 ,it is important1 however1 to remark that if we can thus easily define and measure the difference of entropy between two states of the same body1 the value found depends on the state arbitrarily chosen as the zero point of entropy2 but this is not a very serious difficulty1 and is analogous to that which occurs in the evaluation of other physical magnitudes--temperature1 potential1 etc4 ,a graver difficulty proceeds from its not being possible to define a difference1 or an equality1 of entropy between two bodies chemically different4 ,we are unable1 in fact1 to pass by any means1 reversible or not1 from one to the other1 so long as the transmutation of matter is regarded as impossible2 but it is well understood that it is nevertheless possible to compare the variations of entropy to which these two bodies are both of them individually subject4 ,neither must we conceal from ourselves that the definition supposes1 for a given body1 the possibility of passing from one state to another by a reversible transformation4 ,reversibility is an ideal and extreme case which cannot be realized1 but which can be approximately attained in many circumstances4 ,so with gases and with perfectly elastic bodies1 we effect sensibly reversible transformations1 and changes of physical state are practically reversible4 ,the discoveries of ,sainte-,claire ,deville have brought many chemical phenomena into a similar category1 and reactions such as solution1 which used to be formerly the type of an irreversible phenomenon1 may now often be effected by sensibly reversible means4 ,be that as it may1 when once the definition is admitted1 we arrive1 by taking as a basis the principles set forth at the inception1 at the demonstration of the celebrated theorem of ,clausius3 ,the entropy of a thermally isolated system continues to increase incessantly4 ,it is very evident that the theorem can only be worth applying in cases where the entropy can be exactly defined2 but1 even when thus limited1 the field still remains vast1 and the harvest which we can there reap is very abundant4 ,entropy appears1 then1 as a magnitude measuring in a certain way the evolution of a system1 or1 at least1 as giving the direction of this evolution4 ,this very important consequence certainly did not escape ,clausius1 since the very name of entropy1 which he chose to designate this magnitude1 itself signifies evolution4 ,we have succeeded in defining this entropy by demonstrating1 as has been said1 a certain number of propositions which spring from the postulate of ,clausius2 it is1 therefore1 natural to suppose that this postulate itself contains in potentia the very idea of a necessary evolution of physical systems4 ,but as it was first enunciated1 it contains it in a deeply hidden way4 ,no doubt we should make the principle of ,carnot appear in an interesting light by endeavouring to disengage this fundamental idea1 and by placing it1 as it were1 in large letters4 ,just as1 in elementary geometry1 we can replace the postulate of ,euclid by other equivalent propositions1 so the postulate of thermodynamics is not necessarily fixed1 and it is instructive to try to give it the most general and suggestive character4 ,,mm4 ,perrin and ,langevin have made a successful attempt in this direction4 ,m4 ,perrin enunciates the following principle3 ,an isolated system never passes twice through the same state4 ,in this form1 the principle affirms that there exists a necessary order in the succession of two phenomena2 that evolution takes place in a determined direction4 ,if you prefer it1 it may be thus stated3 ,of two converse transformations unaccompanied by any external effect1 one only is possible4 ,for instance1 two gases may diffuse themselves one in the other in constant volume1 but they could not conversely separate themselves spontaneously4 ,starting from the principle thus put forward1 we make the logical deduction that one cannot hope to construct an engine which should work for an indefinite time by heating a hot source and by cooling a cold one4 ,we thus come again into the route traced by ,clausius1 and from this point we may follow it strictly4 ,whatever the point of view adopted1 whether we regard the proposition of ,m4 ,perrin as the corollary of another experimental postulate1 or whether we consider it as a truth which we admit a priori and verify through its consequences1 we are led to consider that in its entirety the principle of ,carnot resolves itself into the idea that we cannot go back along the course of life1 and that the evolution of a system must follow its necessary progress4 ,clausius and ,lord ,kelvin have drawn from these considerations certain well-known consequences on the evolution of the ,universe4 ,noticing that entropy is a property added to matter1 they admit that there is in the world a total amount of entropy2 and as all real changes which are produced in any system correspond to an increase of entropy1 it may be said that the entropy of the world is continually increasing4 ,thus the quantity of energy existing in the ,universe remains constant1 but transforms itself little by little into heat uniformly distributed at a temperature everywhere identical4 ,in the end1 therefore1 there will be neither chemical phenomena nor manifestation of life2 the world will still exist1 but without motion1 and1 so to speak1 dead4 ,these consequences must be admitted to be very doubtful2 we cannot in any certain way apply to the ,universe1 which is not a finite system1 a proposition demonstrated1 and that not unreservedly1 in the sharply limited case of a finite system4 ,herbert ,spencer1 moreover1 in his book on ,first ,principles1 brings out with much force the idea that1 even if the ,universe came to an end1 nothing would allow us to conclude that1 once at rest1 it would remain so indefinitely4 ,we may recognise that the state in which we are began at the end of a former evolutionary period1 and that the end of the existing era will mark the beginning of a new one4 ,like an elastic and mobile object which1 thrown into the air1 attains by degrees the summit of its course1 then possesses a zero velocity and is for a moment in equilibrium1 and then falls on touching the ground to rebound1 so the world should be subjected to huge oscillations which first bring it to a maximum of entropy till the moment when there should be produced a slow evolution in the contrary direction bringing it back to the state from which it started4 ,thus1 in the infinity of time1 the life of the ,universe proceeds without real stop4 ,this conception is1 moreover1 in accordance with the view certain physicists take of the principle of ,carnot4 ,we shall see1 for example1 that in the kinetic theory we are led to admit that1 after waiting sufficiently long1 we can witness the return of the various states through which a mass of gas1 for example1 has passed in its series of transformations4 ,if we keep to the present era1 evolution has a fixed direction--that which leads to an increase of entropy2 and it is possible to enquire1 in any given system to what physical manifestations this increase corresponds4 ,we note that kinetic1 potential1 electrical1 and chemical forms of energy have a great tendency to transform themselves into calorific energy4 ,a chemical reaction1 for example1 gives out energy2 but if the reaction is not produced under very special conditions1 this energy immediately passes into the calorific form4 ,this is so true1 that chemists currently speak of the heat given out by reactions instead of regarding the energy disengaged in general4 ,in all these transformations the calorific energy obtained has not1 from a practical point of view1 the same value at which it started4 ,one cannot1 in fact1 according to the principle of ,carnot1 transform it integrally into mechanical energy1 since the heat possessed by a body can only yield work on condition that a part of it falls on a body with a lower temperature4 ,thus appears the idea that energies which exchange with each other and correspond to equal quantities have not the same qualitative value4 ,form has its importance1 and there are persons who prefer a golden louis to four pieces of five francs4 ,the principle of ,carnot would thus lead us to consider a certain classification of energies1 and would show us that1 in the transformations possible1 these energies always tend to a sort of diminution of quality--that is1 to a degradation4 ,it would thus reintroduce an element of differentiation of which it seems very difficult to give a mechanical explanation4 ,certain philosophers and physicists see in this fact a reason which condemns a priori all attempts made to give a mechanical explanation of the principle of ,carnot4 ,it is right1 however1 not to exaggerate the importance that should be attributed to the phrase degraded energy4 ,if the heat is not equivalent to the work1 if heat at #ii is not equivalent to heat at #ajj1 that means that we cannot in practice construct an engine which shall transform all this heat into work1 or that1 for the same cold source1 the output is greater when the temperature of the hot source is higher2 but if it were possible that this cold source had itself the temperature of absolute zero1 the whole heat would reappear in the form of work4 ,the case here considered is an ideal and extreme case1 and we naturally cannot realize it2 but this consideration suffices to make it plain that the classification of energies is a little arbitrary and depends more1 perhaps1 on the conditions in which mankind lives than on the inmost nature of things4 ,in fact1 the attempts which have often been made to refer the principle of ,carnot to mechanics have not given convincing results4 ,it has nearly always been necessary to introduce into the attempt some new hypothesis independent of the fundamental hypotheses of ordinary mechanics1 and equivalent1 in reality1 to one of the postulates on which the ordinary exposition of the second law of thermodynamics is founded4 ,helmholtz1 in a justly celebrated theory1 endeavoured to fit the principle of ,carnot into the principle of least action2 but the difficulties regarding the mechanical interpretation of the irreversibility of physical phenomena remain entire4 ,looking at the question1 however1 from the point of view at which the partisans of the kinetic theories of matter place themselves1 the principle is viewed in a new aspect4 ,gibbs and afterwards ,boltzmann and ,professor ,planck have put forward some very interesting ideas on this subject4 ,by following the route they have traced1 we come to consider the principle as pointing out to us that a given system tends towards the configuration presented by the maximum probability1 and1 numerically1 the entropy would even be the logarithm of this probability4 ,thus two different gaseous masses1 enclosed in two separate receptacles which have just been placed in communication1 diffuse themselves one through the other1 and it is highly improbable that1 in their mutual shocks1 both kinds of molecules should take a distribution of velocities which reduce them by a spontaneous phenomenon to the initial state4 ,we should have to wait a very long time for so extraordinary a concourse of circumstances1 but1 in strictness1 it would not be impossible4 ,the principle would only be a law of probability4 ,yet this probability is all the greater the more considerable is the number of molecules itself4 ,in the phenomena habitually dealt with1 this number is such that1 practically1 the variation of entropy in a constant sense takes1 so to speak1 the character of absolute certainty4 ,but there may be exceptional cases where the complexity of the system becomes insufficient for the application of the principle of ,carnot2-- as in the case of the curious movements of small particles suspended in a liquid which are known by the name of ,brownian movements and can be observed under the microscope4 ,the agitation here really seems1 as ,m4 ,gouy has remarked1 to be produced and continued indefinitely1 regardless of any difference in temperature2 and we seem to witness the incessant motion1 in an isothermal medium1 of the particles which constitute matter4 ,perhaps1 however1 we find ourselves already in conditions where the too great simplicity of the distribution of the molecules deprives the principle of its value4 ,m4 ,lippmann has in the same way shown that1 on the kinetic hypothesis1 it is possible to construct such mechanisms that we can so take cognizance of molecular movements that vis viva can be taken from them4 ,the mechanisms of ,m4 ,lippmann are not1 like the celebrated apparatus at one time devised by ,maxwell1 purely hypothetical4 ,they do not suppose a partition with a hole impossible to be bored through matter where the molecular spaces would be larger than the hole itself4 ,they have finite dimensions4 ,thus ,m4 ,lippmann considers a vase full of oxygen at a constant temperature4 ,in the interior of this vase is placed a small copper ring1 and the whole is set in a magnetic field4 ,the oxygen molecules are1 as we know1 magnetic1 and when passing through the interior of the ring they produce in this ring an induced current4 ,during this time1 it is true1 other molecules emerge from the space enclosed by the circuit2 but the two effects do not counterbalance each other1 and the resulting current is maintained4 ,there is elevation of temperature in the circuit in accordance with ,joule's law2 and this phenomenon1 under such conditions1 is incompatible with the principle of ,carnot4 ,it is possible--and that1 ,i think1 is ,m4 ,lippmann's idea--to draw from his very ingenious criticism an objection to the kinetic theory1 if we admit the absolute value of the principle2 but we may also suppose that here again we are in presence of a system where the prescribed conditions diminish the complexity and render it1 consequently1 less probable that the evolution is always effected in the same direction4 ,in whatever way you look at it1 the principle of ,carnot furnishes1 in the immense majority of cases1 a very sure guide in which physicists continue to have the most entire confidence4 #d4 ,,thermodynamics ,to apply the two fundamental principles of thermodynamics1 various methods may be employed1 equivalent in the main1 but presenting as the cases vary a greater or less convenience4 ,in recording1 with the aid of the two quantities1 energy and entropy1 the relations which translate analytically the two principles1 we obtain two relations between the coefficients which occur in a given phenomenon2 but it may be easier and also more suggestive to employ various functions of these quantities4 ,in a memoir1 of which some extracts appeared as early as #ahfi1 a modest scholar1 ,m4 ,massieu1 indicated in particular a remarkable function which he termed a characteristic function1 and by the employment of which calculations are simplified in certain cases4 ,in the same way ,j4,w4 ,gibbs1 in #ahge and #ahgh1 then ,helmholtz in #ahhb1 and1 in ,france1 ,m4 ,duhem1 from the year #ahhf onward1 have published works1 at first ill understood1 of which the renown was1 however1 considerable in the sequel1 and in which they made use of analogous functions under the names of available energy1 free energy1 or internal thermodynamic potential4 ,the magnitude thus designated1 attaching1 as a consequence of the two principles1 to all states of the system1 is perfectly determined when the temperature and other normal variables are known4 ,it allows us1 by calculations often very easy1 to fix the conditions necessary and sufficient for the maintenance of the system in equilibrium by foreign bodies taken at the same temperature as itself4 ,one may hope to constitute in this way1 as ,m4 ,duhem in a long and remarkable series of operations has specially endeavoured to do1 a sort of general mechanics which will enable questions of statics to be treated with accuracy1 and all the conditions of equilibrium of the system1 including the calorific properties1 to be determined4 ,thus1 ordinary statics teaches us that a liquid with its vapour on the top forms a system in equilibrium1 if we apply to the two fluids a pressure depending on temperature alone4 ,thermodynamics will furnish us1 in addition1 with the expression of the heat of vaporization and of1 the specific heats of the two saturated fluids4 ,this new study has given us also most valuable information on compressible fluids and on the theory of elastic equilibrium4 ,added to certain hypotheses on electric or magnetic phenomena1 it gives a coherent whole from which can be deduced the conditions of electric or magnetic equilibrium2 and it illuminates with a brilliant light the calorific laws of electrolytic phenomena4 ,but the most indisputable triumph of this thermodynamic statics is the discovery of the laws which regulate the changes of physical state or of chemical constitution4 ,j4,w4 ,gibbs was the author of this immense progress4 ,his memoir1 now celebrated1 on the equilibrium of heterogeneous substances1 concealed in #ahgf in a review at that time of limited circulation1 and rather heavy to read1 seemed only to contain algebraic theorems applicable with difficulty to reality4 ,it is known that ,helmholtz independently succeeded1 a few years later1 in introducing thermodynamics into the domain of chemistry by his conception of the division of energy into free and into bound energy3 the first1 capable of undergoing all transformations1 and particularly of transforming itself into external action2 the second1 on the other hand1 bound1 and only manifesting itself by giving out heat4 ,when we measure chemical energy1 we ordinarily let it fall wholly into the calorific form2 but1 in reality1 it itself includes both parts1 and it is the variation of the free energy and not that of the total energy measured by the integral disengagement of heat1 the sign of which determines the direction in which the reactions are effected4 ,but if the principle thus enunciated by ,helmholtz as a consequence of the laws of thermodynamics is at bottom identical with that discovered by ,gibbs1 it is more difficult of application and is presented under a more mysterious aspect4 ,it was not until ,m4 ,van der ,waals exhumed the memoir of ,gibbs1 when numerous physicists or chemists1 most of them ,dutch--,professor ,van t',hoff1 ,bakhius ,roozeboom1 and others--utilized the rules set forth in this memoir for the discussion of the most complicated chemical reactions1 that the extent of the new laws was fully understood4 ,the chief rule of ,gibbs is the one so celebrated at the present day under the name of the ,phase ,law4 ,we know that by phases are designated the homogeneous substances into which a system is divided2 thus carbonate of lime1 lime1 and carbonic acid gas are the three phases of a system which comprises ,iceland spar partially dissociated into lime and carbonic acid gas4 ,the number of phases added to the number of independent components--that is to say1 bodies whose mass is left arbitrary by the chemical formulas of the substances entering into the reaction--fixes the general form of the law of equilibrium of the system2 that is to say1 the number of quantities which1 by their variations 7temperature and pressure71 would be of a nature to modify its equilibrium by modifying the constitution of the phases4 ,several authors1 ,m4 ,raveau in particular1 have indeed given very simple demonstrations of this law which are not based on thermodynamics2 but thermodynamics1 which led to its discovery1 continues to give it its true scope4 ,moreover1 it would not suffice merely to determine quantitatively those laws of which it makes known the general form4 ,we must1 if we wish to penetrate deeper into details1 particularize the hypothesis1 and admit1 for instance1 with ,gibbs that we are dealing with perfect gases2 while1 thanks to thermodynamics1 we can constitute a complete theory of dissociation which leads to formulas in complete accord with the numerical results of the experiment4 ,we can thus follow closely all questions concerning the displacements of the equilibrium1 and find a relation of the first importance between the masses of the bodies which react in order to constitute a system in equilibrium4 ,the statics thus constructed constitutes at the present day an important edifice to be henceforth classed amongst historical monuments4 ,some theorists even wish to go a step beyond4 ,they have attempted to begin by the same means a more complete study of those systems whose state changes from one moment to another4 ,this is1 moreover1 a study which is necessary to complete satisfactorily the study of equilibrium itself2 for without it grave doubts would exist as to the conditions of stability1 and it alone can give their true meaning to questions relating to displacements of equilibrium4 ,the problems with which we are thus confronted are singularly difficult4 ,m4 ,duhem has given us many excellent examples of the fecundity of the method2 but if thermodynamic statics may be considered definitely founded1 it cannot be said that the general dynamics of systems1 considered as the study of thermal movements and variations1 are yet as solidly established4 #e4 ,,atomism ,it may appear singularly paradoxical that1 in a chapter devoted to general views on the principles of physics1 a few words should be introduced on the atomic theories of matter4 ,very often1 in fact1 what is called the physics of principles is set in opposition to the hypotheses on the constitution of matter1 particularly to atomic theories4 ,i have already said that1 abandoning the investigation of the unfathomable mystery of the constitution of the ,universe1 some physicists think they may find1 in certain general principles1 sufficient guides to conduct them across the physical world4 ,but ,i have also said1 in examining the history of those principles1 that if they are to-day considered experimental truths1 independent of all theories relating to matter1 they have1 in fact1 nearly all been discovered by scholars who relied on molecular hypotheses3 and the question suggests itself whether this is mere chance1 or whether this chance may not be ordained by higher reasons4 ,in a very profound work which appeared a few years ago1 entitled ,essai critique sur l'hypothese des atomes1 ,m4 ,hannequin1 a philosopher who is also an erudite scholar1 examined the part taken by atomism in the history of science4 ,he notes that atomism and science were born1 in ,greece1 of the same problem1 and that in modern times the revival of the one was closely connected with that of the other4 ,he shows1 too1 by very close analysis1 that the atomic hypothesis is essential to the optics of ,fresnel and of ,cauchy2 that it penetrates into the study of heat2 and that1 in its general features1 it presided at the birth of modern chemistry and is linked with all its progress4 ,he concludes that it is1 in a manner1 the soul of our knowledge of ,nature1 and that contemporary theories are on this point in accord with history3 for these theories consecrate the preponderance of this hypothesis in the domain of science4 ,if ,m4 ,hannequin had not been prematurely cut off in the full expansion of his vigorous talent1 he might have added another chapter to his excellent book4 ,he would have witnessed a prodigious budding of atomistic ideas1 accompanied1 it is true1 by wide modifications in the manner in which the atom is to be regarded1 since the most recent theories make material atoms into centres constituted of atoms of electricity4 ,on the other hand1 he would have found in the bursting forth of these new doctrines one more proof in support of his idea that science is indissolubly bound to atomism4 ,from the philosophical point of view1 ,m4 ,hannequin1 examining the reasons which may have called these links into being1 arrives at the idea that they necessarily proceed from the constitution of our knowledge1 or1 perhaps1 from that of ,nature itself4 ,moreover1 this origin1 double in appearance1 is single at bottom4 ,our minds could not1 in fact1 detach and come out of themselves to grasp reality and the absolute in ,nature4 ,according to the idea of ,descartes1 it is the destiny of our minds only to take hold of and to understand that which proceeds from them4 ,thus atomism1 which is1 perhaps1 only an appearance containing even some contradictions1 is yet a well-founded appearance1 since it conforms to the laws of our minds2 and this hypothesis is1 in a way1 necessary4 ,we may dispute the conclusions of ,m4 ,hannequin1 but no one will refuse to recognise1 as he does1 that atomic theories occupy a preponderating part in the doctrines of physics2 and the position which they have thus conquered gives them1 in a way1 the right of saying that they rest on a real principle4 ,it is in order to recognise this right that several physicists--,m4 ,langevin1 for example--ask that atoms be promoted from the rank of hypotheses to that of principles4 ,by this they mean that the atomistic ideas forced upon us by an almost obligatory induction based on very exact experiments1 enable us to co-ordinate a considerable amount of facts1 to construct a very general synthesis1 and to foresee a great number of phenomena4 ,it is of moment1 moreover1 to thoroughly understand that atomism does not necessarily set up the hypothesis of centres of attraction acting at a distance1 and it must not be confused with molecular physics1 which has1 on the other hand1 undergone very serious checks4 ,the molecular physics greatly in favour some fifty years ago leads to such complex representations and to solutions often so undetermined1 that the most courageous are wearied with upholding it and it has fallen into some discredit4 ,it rested on the fundamental principles of mechanics applied to molecular actions2 and that was1 no doubt1 an extension legitimate enough1 since mechanics is itself only an experimental science1 and its principles1 established for the movements of matter taken as a whole1 should not be applied outside the domain which belongs to them4 ,atomism1 in fact1 tends more and more1 in modern theories1 to imitate the principle of the conservation of energy or that of entropy1 to disengage itself from the artificial bonds which attached it to mechanics1 and to put itself forward as an independent principle4 ,atomistic ideas also have undergone evolution1 and this slow evolution has been considerably quickened under the influence of modern discoveries4 ,these reach back to the most remote antiquity1 and to follow their development we should have to write the history of human thought which they have always accompanied since the time of ,leucippus1 ,democritus1 ,epicurus1 and ,lucretius4 ,the first observers who noticed that the volume of a body could be diminished by compression or cold1 or augmented by heat1 and who saw a soluble solid body mix completely with the water which dissolved it1 must have been compelled to suppose that matter was not dispersed continuously throughout the space it seemed to occupy4 ,they were thus brought to consider it discontinuous1 and to admit that a substance having the same composition and the same properties in all its parts--in a word1 perfectly homogeneous--ceases to present this homogeneity when considered within a sufficiently small volume4 ,modern experimenters have succeeded by direct experiments in placing in evidence this heterogeneous character of matter when taken in small mass4 ,thus1 for example1 the superficial tension1 which is constant for the same liquid at a given temperature1 no longer has the same value when the thickness of the layer of liquid becomes extremely small4 ,newton noticed even in his time that a dark zone is seen to form on a soap bubble at the moment when it becomes so thin that it must burst4 ,professor ,reinold and ,sir ,arthur ,rcker have shown that this zone is no longer exactly spherical2 and from this we must conclude that the superficial tension1 constant for all thicknesses above a certain limit1 commences to vary when the thickness falls below a critical value1 which these authors estimate1 on optical grounds1 at about fifty millionths of a millimetre4 ,from experiments on capillarity1 ,prof4 ,quincke has obtained similar results with regard to layers of solids4 ,but it is not only capillary properties which allow this characteristic to be revealed4 ,all the properties of a body are modified when taken in small mass2 ,m4 ,meslin proves this in a very ingenious way as regards optical properties1 and ,mr ,vincent in respect of electric conductivity4 ,m4 ,houllevigue1 who1 in a chapter of his excellent work1 ,du ,laboratoire l',usine1 has very clearly set forth the most interesting considerations on atomic hypotheses1 has recently demonstrated that copper and silver cease to combine with iodine as soon as they are present in a thickness of less than thirty millionths of a millimetre4 ,it is this same dimension likewise that is possessed1 according to ,m4 ,wiener1 by the smallest thicknesses it is possible to deposit on glass4 ,these layers are so thin that they cannot be perceived1 but their presence is revealed by a change in the properties of the light reflected by them4 ,thus1 below fifty to thirty millionths of a millimetre the properties of matter depend on its thickness4 ,there are then1 no doubt1 only a few molecules to be met with1 and it may be concluded1 in consequence1 that the discontinuous elements of bodies--that is1 the molecules-- have linear dimensions of the order of magnitude of the millionth of a millimetre4 ,considerations regarding more complex phenomena1 for instance the phenomena of electricity by contact1 and also the kinetic theory of gases1 bring us to the same conclusion4 ,the idea of the discontinuity of matter forces itself upon us for many other reasons4 ,all modern chemistry is founded on this principle2 and laws like the law of multiple proportions1 introduce an evident discontinuity to which we find analogies in the law of electrolysis4 ,the elements of bodies we are thus brought to regard might1 as regards solids at all events1 be considered as immobile2 but this immobility could not explain the phenomena of heat1 and1 as it is entirely inadmissible for gases1 it seems very improbable it can absolutely occur in any state4 ,we are thus led to suppose that these elements are animated by very complicated movements1 each one proceeding in closed trajectories in which the least variations of temperature or pressure cause modifications4 ,the atomistic hypothesis shows itself remarkably fecund in the study of phenomena produced in gases1 and here the mutual independence of the particles renders the question relatively more simple and1 perhaps1 allows the principles of mechanics to be more certainly extended to the movements of molecules4 ,the kinetic theory of gases can point to unquestioned successes2 and the idea of ,daniel ,bernouilli1 who1 as early as #agch1 considered a gaseous mass to be formed of a considerable number of molecules animated by rapid movements of translation1 has been put into a form precise enough for mathematical analysis1 and we have thus found ourselves in a position to construct a really solid foundation4 ,it will be at once conceived1 on this hypothesis1 that pressure is the resultant of the shocks of the molecules against the walls of the containing vessel1 and we at once come to the demonstration that the law of ,mariotte is a natural consequence of this origin of pressure2 since1 if the volume occupied by a certain number of molecules is doubled1 the number of shocks per second on each square centimetre of the walls becomes half as much4 ,but if we attempt to carry this further1 we find ourselves in presence of a serious difficulty4 ,it is impossible to mentally follow every one of the many individual molecules which compose even a very limited mass of gas4 ,the path followed by this molecule may be every instant modified by the chance of running against another1 or by a shock which may make it rebound in another direction4 ,the difficulty would be insoluble if chance had not laws of its own4 ,it was ,maxwell who first thought of introducing into the kinetic theory the calculation of probabilities4 ,willard ,gibbs and ,boltzmann later on developed this idea1 and have founded a statistical method which does not1 perhaps1 give absolute certainty1 but which is certainly most interesting and curious4 ,molecules are grouped in such a way that those belonging to the same group may be considered as having the same state of movement2 then an examination is made of the number of molecules in each group1 and what are the changes in this number from one moment to another4 ,it is thus often possible to determine the part which the different groups have in the total properties of the system and in the phenomena which may occur4 ,such a method1 analogous to the one employed by statisticians for following the social phenomena in a population1 is all the more legitimate the greater the number of individuals counted in the averages2 now1 the number of molecules contained in a limited space-- for example1 in a centimetre cube taken in normal conditions--is such that no population could ever attain so high a figure4 ,all considerations1 those we have indicated as well as others which might be invoked 7for example1 the recent researches of ,m4 ,spring on the limit of visibility of fluorescence71 give this result3--that there are1 in this space1 some twenty thousand millions of molecules4 ,each of these must receive in the space of a millimetre about ten thousand shocks1 and be ten thousand times thrust out of its course4 ,the free path of a molecule is then very small1 but it can be singularly augmented by diminishing the number of them4 ,tait and ,dewar have calculated that1 in a good modern vacuum1 the length of the free path of the remaining molecules not taken away by the air-pump easily reaches a few centimetres4 ,by developing this theory1 we come to consider that1 for a given temperature1 every molecule 7and even every individual particle1 atom1 or ion7 which takes part in the movement has1 on the average1 the same kinetic energy in every body1 and that this energy is proportional to the absolute temperature2 so that it is represented by this temperature multiplied by a constant quantity which is a universal constant4 ,this result is not an hypothesis but a very great probability4 ,this probability increases when it is noted that the same value for the constant is met with in the study of very varied phenomena2 for example1 in certain theories on radiation4 ,knowing the mass and energy of a molecule1 it is easy to calculate its speed2 and we find that the average speed is about #djj metres per second for carbonic anhydride1 #ejj for nitrogen1 and #ahej for hydrogen at #j ,c4 and at ordinary pressure4 ,i shall have occasion1 later on1 to speak of much more considerable speeds than these as animating other particles4 ,the kinetic theory has permitted the diffusion of gases to be explained1 and the divers circumstances of the phenomenon to be calculated4 ,it has allowed us to show1 as ,m4 ,brillouin has done1 that the coefficient of diffusion of two gases does not depend on the proportion of the gases in the mixture2 it gives a very striking image of the phenomena of viscosity and conductivity2 and it leads us to think that the coefficients of friction and of conductivity are independent of the density2 while all these previsions have been verified by experiment4 ,it has also invaded optics2 and by relying on the principle of ,doppler1 ,professor ,michelson has succeeded in obtaining from it an explanation of the length presented by the spectral rays of even the most rarefied gases4 ,but however interesting are these results1 they would not have sufficed to overcome the repugnance of certain physicists for speculations which1 an imposing mathematical baggage notwithstanding1 seemed to them too hypothetical4 ,the theory1 moreover1 stopped at the molecule1 and appeared to suggest no idea which could lead to the discovery of the key to the phenomena where molecules exercise a mutual influence on each other4 ,the kinetic hypothesis1 therefore1 remained in some disfavour with a great number of persons1 particularly in ,france1 until the last few years1 when all the recent discoveries of the conductivity of gases and of the new radiations came to procure for it a new and luxuriant efflorescence4 ,it may be said that the atomistic synthesis1 but yesterday so decried1 is to-day triumphant4 ,the elements which enter into the earlier kinetic theory1 and which1 to avoid confusion1 should be always designated by the name of molecules1 were not1 truth to say1 in the eyes of the chemists1 the final term of the divisibility of matter4 ,it is well known that1 to them1 except in certain particular bodies like the vapour of mercury and argon1 the molecule comprises several atoms1 and that1 in compound bodies1 the number of these atoms may even be fairly considerable4 ,but physicists rarely needed to have recourse to the consideration of these atoms4 ,they spoke of them to explain certain particularities of the propagation of sound1 and to enunciate laws relating to specific heats2 but1 in general1 they stopped at the consideration of the molecule4 ,the present theories carry the division much further4 ,i shall not dwell now on these theories1 since1 in order to thoroughly understand them1 many other facts must be examined4 ,but to avoid all confusion1 it remains understood that1 contrary1 no doubt1 to etymology1 but in conformity with present custom1 ,i shall continue in what follows to call atoms those particles of matter which have till now been spoken of2 these atoms being themselves1 according to modern views1 singularly complex edifices formed of elements1 of which we shall have occasion to indicate the nature later4 ,,chapter ,,iv ,,the ,,various ,,states ,,of ,,matter #a4 ,,the ,,statics ,,of ,,fluids ,the division of bodies into gaseous1 liquid1 and solid1 and the distinction established for the same substance between the three states1 retain a great importance for the applications and usages of daily life1 but have long since lost their absolute value from the scientific point of view4 ,so far as concerns the liquid and gaseous states particularly1 the already antiquated researches of ,andrews confirmed the ideas of ,cagniard de la ,tour and established the continuity of the two states4 ,a group of physical studies has thus been constituted on what may be called the statics of fluids1 in which we examine the relations existing between the pressure1 the volume1 and the temperature of bodies1 and in which are comprised1 under the term fluid1 gases as well as liquids4 ,these researches deserve attention by their interest and the generality of the results to which they have led4 ,they also give a remarkable example of the happy effects which may be obtained by the combined employment of the various methods of investigation used in exploring the domain of nature4 ,thermodynamics has1 in fact1 allowed us to obtain numerical relations between the various coefficients1 and atomic hypotheses have led to the establishment of one capital relation1 the characteristic equation of fluids2 while1 on the other hand1 experiment in which the progress made in the art of measurement has been utilized1 has furnished the most valuable information on all the laws of compressibility and dilatation4 ,the classical work of ,andrews was not very wide4 ,andrews did not go much beyond pressures close to the normal and ordinary temperatures4 ,of late years several very interesting and peculiar cases have been examined by ,,mm4 ,cailletet1 ,mathias1 ,batelli1 ,leduc1 ,p4 ,chappuis1 and other physicists4 ,sir ,w4 ,ramsay and ,mr ,s4 ,young have made known the isothermal diagrams#f of a certain number of liquid bodies at the ordinary temperature4 ,they have thus been able1 while keeping to somewhat restricted limits of temperature and pressure1 to touch upon the most important questions1 since they found themselves in the region of the saturation curve and of the critical point4 ,footnote #f3 ,by isothermal diagram is meant the pattern or complex formed when the isothermal lines are arranged in curves of which the pressure is the ordinate and the volume the abscissa4--,,ed4 ,but the most complete and systematic body of researches is due to ,m4 ,amagat1 who undertook the study of a certain number of bodies1 some liquid and some gaseous1 extending the scope of his experiments so as to embrace the different phases of the phenomena and to compare together1 not only the results relating to the same bodies1 but also those concerning different bodies which happen to be in the same conditions of temperature and pressure1 but in very different conditions as regards their critical points4 ,from the experimental point of view1 ,m4 ,amagat has been able1 with extreme skill1 to conquer the most serious difficulties4 ,he has managed to measure with precision pressures amounting to #cjjj atmospheres1 and also the very small volumes then occupied by the fluid mass under consideration4 ,this last measurement1 which necessitates numerous corrections1 is the most delicate part of the operation4 ,these researches have dealt with a certain number of different bodies4 ,those relating to carbonic acid and ethylene take in the critical point4 ,others1 on hydrogen and nitrogen1 for instance1 are very extended4 ,others1 again1 such as the study of the compressibility of water1 have a special interest1 on account of the peculiar properties of this substance4 ,m4 ,amagat1 by a very concise discussion of the experiments1 has also been able to definitely establish the laws of compressibility and dilatation of fluids under constant pressure1 and to determine the value of the various coefficients as well as their variations4 ,it ought to be possible to condense all these results into a single formula representing the volume1 the temperature1 and the pressure4 ,rankin and1 subsequently1 ,recknagel1 and then ,hirn1 formerly proposed formulas of that kind2 but the most famous1 the one which first appeared to contain in a satisfactory manner all the facts which experiments brought to light and led to the production of many others1 was the celebrated equation of ,van der ,waals4 ,professor ,van der ,waals arrived at this relation by relying upon considerations derived from the kinetic theory of gases4 ,if we keep to the simple idea at the bottom of this theory1 we at once demonstrate that the gas ought to obey the laws of ,mariotte and of ,gay-,lussac1 so that the characteristic equation would be obtained by the statement that the product of the number which is the measure of the volume by that which is the measure of the pressure is equal to a constant coefficient multiplied by the degree of the absolute temperature4 ,but to get at this result we neglect two important factors4 ,we do not take into account1 in fact1 the attraction which the molecules must exercise on each other4 ,now1 this attraction1 which is never absolutely non-existent1 may become considerable when the molecules are drawn closer together2 that is to say1 when the compressed gaseous mass occupies a more and more restricted volume4 ,on the other hand1 we assimilate the molecules1 as a first approximation1 to material points without dimensions2 in the evaluation of the path traversed by each molecule no notice is taken of the fact that1 at the moment of the shock1 their centres of gravity are still separated by a distance equal to twice the radius of the molecule4 ,m4 ,van der ,waals has sought out the modifications which must be introduced into the simple characteristic equation to bring it nearer to reality4 ,he extends to the case of gases the considerations by which ,laplace1 in his famous theory of capillarity1 reduced the effect of the molecular attraction to a perpendicular pressure exercised on the surface of a liquid4 ,this leads him to add to the external pressure1 that due to the reciprocal attractions of the gaseous particles4 ,on the other hand1 when we attribute finite dimensions to these particles1 we must give a higher value to the number of shocks produced in a given time1 since the effect of these dimensions is to diminish the mean path they traverse in the time which elapses between two consecutive shocks4 ,the calculation thus pursued leads to our adding to the pressure in the simple equation a term which is designated the internal pressure1 and which is the quotient of a constant by the square of the volume2 also to our deducting from the volume a constant which is the quadruple of the total and invariable volume which the gaseous molecules would occupy did they touch one another4 ,the experiments fit in fairly well with the formula of ,van der ,waals1 but considerable discrepancies occur when we extend its limits1 particularly when the pressures throughout a rather wider interval are considered2 so that other and rather more complex formulas1 on which there is no advantage in dwelling1 have been proposed1 and1 in certain cases1 better represent the facts4 ,but the most remarkable result of ,m4 ,van der ,waals' calculations is the discovery of corresponding states4 ,for a long time physicists spoke of bodies taken in a comparable state4 ,dalton1 for example1 pointed out that liquids have vapour-pressures equal to the temperatures equally distant from their boiling-point2 but that if1 in this particular property1 liquids were comparable under these conditions of temperature1 as regards other properties the parallelism was no longer to be verified4 ,no general rule was found until ,m4 ,van der ,waals first enunciated a primary law1 viz41 that if the pressure1 the volume1 and the temperature are estimated by taking as units the critical quantities1 the constants special to each body disappear in the characteristic equation1 which thus becomes the same for all fluids4 ,the words corresponding states thus take a perfectly precise signification4 ,corresponding states are those for which the numerical values of the pressure1 volume1 and temperature1 expressed by taking as units the values corresponding to the critical point1 are equal2 and1 in corresponding states any two fluids have exactly the same properties4 ,m4 ,natanson1 and subsequently ,p4 ,curie and ,m4 ,meslin1 have shown by various considerations that the same result may be arrived at by choosing units which correspond to any corresponding states2 it has also been shown that the theorem of corresponding states in no way implies the exactitude of ,van der ,waals' formula4 ,in reality1 this is simply due to the fact that the characteristic equation only contains three constants4 ,the philosophical importance and the practical interest of the discovery nevertheless remain considerable4 ,as was to be expected1 numbers of experimenters have sought whether these consequences are duly verified in reality4 ,m4 ,amagat1 particularly1 has made use for this purpose of a most original and simple method4 ,he remarks that1 in all its generality1 the law may be translated thus3 ,if the isothermal diagrams of two substances be drawn to the same scale1 taking as unit of volume and of pressure the values of the critical constants1 the two diagrams should coincide2 that is to say1 their superposition should present the aspect of one diagram appertaining to a single substance4 ,further1 if we possess the diagrams of two bodies drawn to any scales and referable to any units whatever1 as the changes of units mean changes in the scale of the axes1 we ought to make one of the diagrams similar to the other by lengthening or shortening it in the direction of one of the axes4 ,m4 ,amagat then photographs two isothermal diagrams1 leaving one fixed1 but arranging the other so that it may be free to turn round each axis of the co-ordinates2 and by projecting1 by means of a magic lantern1 the second on the first1 he arrives in certain cases at an almost complete coincidence4 ,this mechanical means of proof thus dispenses with laborious calculations1 but its sensibility is unequally distributed over the different regions of the diagram4 ,m4 ,raveau has pointed out an equally simple way of verifying the law1 by remarking that if the logarithms of the pressure and volume are taken as co-ordinates1 the co-ordinates of two corresponding points differ by two constant quantities1 and the corresponding curves are identical4 ,from these comparisons1 and from other important researches1 among which should be particularly mentioned those of ,mr ,s4 ,young and ,m4 ,mathias1 it results that the laws of corresponding states have not1 unfortunately1 the degree of generality which we at first attributed to them1 but that they are satisfactory when applied to certain groups of bodies4#g ,footnote #g3 ,mr ,preston thus puts it3 ,the law of corresponding states seems to be not quite1 but very nearly true for these substances i4e4 the halogen derivatives of benzene2 but in the case of the other substances examined1 the majority of these generalizations were either only roughly true or altogether departed from 7,theory of ,heat1 ,london1 #aijd1 p4 #ead47--;,,ed4 ,if in the study of the statics of a simple fluid the experimental results are already complex1 we ought to expect much greater difficulties when we come to deal with mixtures2 still the problem has been approached1 and many points are already cleared up4 ,mixed fluids may first of all be regarded as composed of a large number of invariable particles4 ,in this particularly simple case ,m4 ,van der ,waals has established a characteristic equation of the mixtures which is founded on mechanical considerations4 ,various verifications of this formula have been effected1 and it has1 in particular1 been the object of very important remarks by ,m4 ,daniel ,berthelot4 ,it is interesting to note that thermodynamics seems powerless to determine this equation1 for it does not trouble itself about the nature of the bodies obedient to its laws2 but1 on the other hand1 it intervenes to determine the properties of coexisting phases4 ,if we examine the conditions of equilibrium of a mixture which is not subjected to external forces1 it will be demonstrated that the distribution must come back to a juxtaposition of homogeneous phases2 in a given volume1 matter ought so to arrange itself that the total sum of free energy has a minimum value4 ,thus1 in order to elucidate all questions relating to the number and qualities of the phases into which the substance divides itself1 we are led to regard the geometrical surface which for a given temperature represents the free energy4 ,i am unable to enter here into the detail of the questions connected with the theories of ,gibbs1 which have been the object of numerous theoretical studies1 and also of a series1 ever more and more abundant1 of experimental researches4 ,m4 ,duhem1 in particular1 has published1 on the subject1 memoirs of the highest importance1 and a great number of experimenters1 mostly scholars working in the physical laboratory of ,leyden under the guidance of the ,director1 ,mr ,kamerlingh ,onnes1 have endeavoured to verify the anticipations of the theory4 ,we are a little less advanced as regards abnormal substances2 that is to say1 those composed of molecules1 partly simple and partly complex1 and either dissociated or associated4 ,these cases must naturally be governed by very complex laws4 ,recent researches by ,,mm4 ,van der ,waals1 ,alexeif1 ,rothmund1 ,knen1 ,lehfeld1 etc41 throw1 however1 some light on the question4 ,the daily more numerous applications of the laws of corresponding states have rendered highly important the determination of the critical constants which permit these states to be defined4 ,in the case of homogeneous bodies the critical elements have a simple1 clear1 and precise sense2 the critical temperature is that of the single isothermal line which presents a point of inflexion at a horizontal tangent2 the critical pressure and the critical volume are the two co-ordinates of this point of inflexion4 ,the three critical constants may be determined1 as ,mr ,s4 ,young and ,m4 ,amagat have shown1 by a direct method based on the consideration of the saturated states4 ,results1 perhaps more precise1 may also be obtained if one keeps to two constants or even to a single one-- temperature1 for example--by employing various special methods4 ,many others1 ,,mm4 ,cailletet and ,colardeau1 ,m4 ,young1 ,m4,j4 ,chappuis1 etc41 have proceeded thus4 ,the case of mixtures is much more complicated4 ,a binary mixture has a critical space instead of a critical point4 ,this space is comprised between two extreme temperatures1 the lower corresponding to what is called the folding point1 the higher to that which we call the point of contact of the mixture4 ,between these two temperatures an isothermal compression yields a quantity of liquid which increases1 then reaches a maximum1 diminishes1 and disappears4 ,this is the phenomenon of retrograde condensation4 ,we may say that the properties of the critical point of a homogeneous substance are1 in a way1 divided1 when it is a question of a binary mixture1 between the two points mentioned4 ,calculation has enabled ,m4 ,van der ,waals1 by the application of his kinetic theories1 and ,m4 ,duhem1 by means of thermodynamics1 to foresee most of the results which have since been verified by experiment4 ,all these facts have been admirably set forth and systematically co-ordinated by ,m4 ,mathias1 who1 by his own researches1 moreover1 has made contributions of the highest value to the study of questions regarding the continuity of the liquid and gaseous states4 ,the further knowledge of critical elements has allowed the laws of corresponding states to be more closely examined in the case of homogeneous substances4 ,it has shown that1 as ,i have already said1 bodies must be arranged in groups1 and this fact clearly proves that the properties of a given fluid are not determined by its critical constants alone1 and that it is necessary to add to them some other specific parameters2 ,m4 ,mathias and ,m4 ,d4 ,berthelot have indicated some which seem to play a considerable part4 ,it results also from this that the characteristic equation of a fluid cannot yet be considered perfectly known4 ,neither the equation of ,van der ,waals nor the more complicated formulas which have been proposed by various authors are in perfect conformity with reality4 ,we may think that researches of this kind will only be successful if attention is concentrated1 not only on the phenomena of compressibility and dilatation1 but also on the calorimetric properties of bodies4 ,thermodynamics indeed establishes relations between those properties and other constants1 but does not allow everything to be foreseen4 ,several physicists have effected very interesting calorimetric measurements1 either1 like ,m4 ,perot1 in order to verify ,clapeyron's formula regarding the heat of vaporization1 or to ascertain the values of specific heats and their variations when the temperature or the pressure happens to change4 ,m4 ,mathias has even succeeded in completely determining the specific heats of liquefied gases and of their saturated vapours1 as well as the heat of internal and external vaporization4 #b4 ,,the ,,liquefaction ,,of ,,gases1 ,,and ,,the ,,properties ,,of ,,bodies ,,at ,a ,,low ,,temperature ,the scientific advantages of all these researches have been great1 and1 as nearly always happens1 the practical consequences derived from them have also been most important4 ,it is owing to the more complete knowledge of the general properties of fluids that immense progress has been made these last few years in the methods of liquefying gases4 ,from a theoretical point of view the new processes of liquefaction can be classed in two categories4 ,linde's machine and those resembling it utilize1 as is known1 expansion without any notable production of external work4 ,this expansion1 nevertheless1 causes a fall in the temperature1 because the gas in the experiment is not a perfect gas1 and1 by an ingenious process1 the refrigerations produced are made cumulative4 ,several physicists have proposed to employ a method whereby liquefaction should be obtained by expansion with recuperable external work4 ,this method1 proposed as long ago as #ahfj by ,siemens1 would offer considerable advantages4 ,theoretically1 the liquefaction would be more rapid1 and obtained much more economically2 but unfortunately in the experiment serious obstacles are met with1 especially from the difficulty of obtaining a suitable lubricant under intense cold for those parts of the machine which have to be in movement if the apparatus is to work4 ,m4 ,claude has recently made great progress on this point by the use1 during the running of the machine1 of the ether of petrol1 which is uncongealable1 and a good lubricant for the moving parts4 ,when once the desired region of cold is reached1 air itself is used1 which moistens the metals but does not completely avoid friction2 so that the results would have remained only middling1 had not this ingenious physicist devised a new improvement which has some analogy with superheating of steam in steam engines4 ,he slightly varies the initial temperature of the compressed air on the verge of liquefaction so as to avoid a zone of deep perturbations in the properties of fluids1 which would make the work of expansion very feeble and the cold produced consequently slight4 ,this improvement1 simple as it is in appearance1 presents several other advantages which immediately treble the output4 ,the special object of ,m4 ,claude was to obtain oxygen in a practical manner by the actual distillation of liquid air4 ,since nitrogen boils at -#aid and oxygen at -#ahj4e ,c41 if liquid air be evaporated1 the nitrogen escapes1 especially at the commencement of the evaporation1 while the oxygen concentrates in the residual liquid1 which finally consists of pure oxygen1 while at the same time the temperature rises to the boiling-point 7-#ahj4e ,c47 of oxygen4 ,but liquid air is costly1 and if one were content to evaporate it for the purpose of collecting a part of the oxygen in the residuum1 the process would have a very poor result from the commercial point of view4 ,as early as #ahib1 ,mr ,parkinson thought of improving the output by recovering the cold produced by liquid air during its evaporation2 but an incorrect idea1 which seems to have resulted from certain experiments of ,dewar--the idea that the phenomenon of the liquefaction of air would not be1 owing to certain peculiarities1 the exact converse of that of vaporization--led to the employment of very imperfect apparatus4 ,m4 ,claude1 however1 by making use of a method which he calls the reversal#h method1 obtains a complete rectification in a remarkably simple manner and under extremely advantageous economic conditions4 ,apparatus1 of surprisingly reduced dimensions but of great efficiency1 is now in daily work1 which easily enables more than a thousand cubic metres of oxygen to be obtained at the rate1 per horse-power1 of more than a cubic metre per hour4 ,footnote #h3 ,methode avec retour en arriere4--,,ed ,it is in ,england1 thanks to the skill of ,sir ,james ,dewar and his pupils--thanks also1 it must be said1 to the generosity of the ,royal ,institution1 which has devoted considerable sums to these costly experiments--that the most numerous and systematic researches have been effected on the production of intense cold4 ,i shall here note only the more important results1 especially those relating to the properties of bodies at low temperatures4 ,their electrical properties1 in particular1 undergo some interesting modifications4 ,the order which metals assume in point of conductivity is no longer the same as at ordinary temperatures4 ,thus at -#bjj ,c4 copper is a better conductor than silver4 ,the resistance diminishes with the temperature1 and1 down to about -#bjj1 this diminution is almost linear1 and it would seem that the resistance tends towards zero when the temperature approaches the absolute zero4 ,but1 after -#bjj1 the pattern of the curves changes1 and it is easy to foresee that at absolute zero the resistivities of all metals would still have1 contrary to what was formerly supposed1 a notable value4 ,solidified electrolytes which1 at temperatures far below their fusion point1 still retain a very appreciable conductivity1 become1 on the contrary1 perfect insulators at low temperatures4 ,their dielectric constants assume relatively high values4 ,,mm4 ,curie and ,compan1 who have studied this question from their own point of view1 have noted1 moreover1 that the specific inductive capacity changes considerably with the temperature4 ,in the same way1 magnetic properties have been studied4 ,a very interesting result is that found in oxygen3 the magnetic susceptibility of this body increases at the moment of liquefaction4 ,nevertheless1 this increase1 which is enormous 7since the susceptibility becomes sixteen hundred times greater than it was at first71 if we take it in connection with equal volumes1 is much less considerable if taken in equal masses4 ,it must be concluded from this fact that the magnetic properties apparently do not belong to the molecules themselves1 but depend on their state of aggregation4 ,the mechanical properties of bodies also undergo important modifications4 ,in general1 their cohesion is greatly increased1 and the dilatation produced by slight changes of temperature is considerable4 ,sir ,james ,dewar has effected careful measurements of the dilatation of certain bodies at low temperatures3 for example1 of ice4 ,changes in colour occur1 and vermilion and iodide of mercury pass into pale orange4 ,phosphorescence becomes more intense1 and most bodies of complex structure--milk1 eggs1 feathers1 cotton1 and flowers--become phosphorescent4 ,the same is the case with certain simple bodies1 such as oxygen1 which is transformed into ozone and emits a white light in the process4 ,chemical affinity is almost put an end to2 phosphorus and potassium remain inert in liquid oxygen4 ,it should1 however1 be noted1 and this remark has doubtless some interest for the theories of photographic action1 that photographic substances retain1 even at the temperature of liquid hydrogen1 a very considerable part of their sensitiveness to light4 ,sir ,james ,dewar has made some important applications of low temperatures in chemical analysis2 he also utilizes them to create a vacuum4 ,his researches have1 in fact1 proved that the pressure of air congealed by liquid hydrogen cannot exceed the millionth of an atmosphere4 ,we have1 then1 in this process1 an original and rapid means of creating an excellent vacuum in apparatus of very different kinds--a means which1 in certain cases1 may be particularly convenient4#i ,footnote #i3 ,professor ,soddy1 in a paper read before the ,royal ,society on the #aeth ,november #aijf1 warns experimenters against vacua created by charcoal cooled in liquid air 7the method referred-to in the text71 unless as much of the air as possible is first removed with a pump and replaced by some argon-free gas4 ,according to him1 neither helium nor argon is absorbed by charcoal4 ,by the use of electrically-heated calcium1 he claims to have produced an almost perfect vacuum4--,,ed4 ,thanks to these studies1 a considerable field has been opened up for biological research1 but in this1 which is not our subject1 ,i shall notice one point only4 ,it has been proved that vital germs--bacteria1 for example--may be kept for seven days at -#aij;,c4 without their vitality being modified4 ,phosphorescent organisms cease1 it is true1 to shine at the temperature of liquid air1 but this fact is simply due to the oxidations and other chemical reactions which keep up the phosphorescence being then suspended1 for phosphorescent activity reappears so soon as the temperature is again sufficiently raised4 ,an important conclusion has been drawn from these experiments which affects cosmogonical theories3 since the cold of space could not kill the germs of life1 it is in no way absurd to suppose that1 under proper conditions1 a germ may be transmitted from one planet to another4 ,among the discoveries made with the new processes1 the one which most strikingly interested public attention is that of new gases in the atmosphere4 ,we know how ,sir ,william ,ramsay and ,dr4 ,travers first observed by means of the spectroscope the characteristics of the companions of argon in the least volatile part of the atmosphere4 ,sir ,james ,dewar on the one hand1 and ,sir ,william ,ramsay on the other1 subsequently separated in addition to argon and helium1 crypton1 xenon1 and neon4 ,the process employed consists essentially in first solidifying the least volatile part of the air and then causing it to evaporate with extreme slowness4 ,a tube with electrodes enables the spectrum of the gas in process of distillation to be observed4 ,in this manner1 the spectra of the various gases may be seen following one another in the inverse order of their volatility4 ,all these gases are monoatomic1 like mercury2 that is to say1 they are in the most simple state1 they possess no internal molecular energy 7unless it is that which heat is capable of supplying71 and they even seem to have no chemical energy4 ,everything leads to the belief that they show the existence on the earth of an earlier state of things now vanished4 ,it may be supposed1 for instance1 that helium and neon1 of which the molecular mass is very slight1 were formerly more abundant on our planet2 but at an epoch when the temperature of the globe was higher1 the very speed of their molecules may have reached a considerable value1 exceeding1 for instance1 eleven kilometres per second1 which suffices to explain why they should have left our atmosphere4 ,crypton and neon1 which have a density four times greater than oxygen1 may1 on the contrary1 have partly disappeared by solution at the bottom of the sea1 where it is not absurd to suppose that considerable quantities would be found liquefied at great depths4#aj ,footnote #aj3 ,another view1 viz4 that these inert gases are a kind of waste product of radioactive changes1 is also gaining ground4 ,the discovery of the radioactive mineral malacone1 which gives off both helium and argon1 goes to support this4 ,see ,messrs ,ketchin and ,winterson's paper on the subject at the ,chemical ,society1 #ahth ,october #aijf4--;,,ed4 ,it is probable1 moreover1 that the higher regions of the atmosphere are not composed of the same air as that around us4 ,sir ,james ,dewar points out that ,dalton's law demands that every gas composing the atmosphere should have1 at all heights and temperatures1 the same pressure as if it were alone1 the pressure decreasing the less quickly1 all things being equal1 as its density becomes less4 ,it results from this that the temperature becoming gradually lower as we rise in the atmosphere1 at a certain altitude there can no longer remain any traces of oxygen or nitrogen1 which no doubt liquefy1 and the atmosphere must be almost exclusively composed of the most volatile gases1 including hydrogen1 which ,m4,a4 ,gautier has1 like ,lord ,rayleigh and ,sir ,william ,ramsay1 proved to exist in the air4 ,the spectrum of the ,aurora borealis1 in which are found the lines of those parts of the atmosphere which cannot be liquefied in liquid hydrogen1 together with the lines of argon1 crypton1 and xenon1 is quite in conformity with this point of view4 ,it is1 however1 singular that it should be the spectrum of crypton1 that is to say1 of the heaviest gas of the group1 which appears most clearly in the upper regions of the atmosphere4 ,among the gases most difficult to liquefy1 hydrogen has been the object of particular research and of really quantitative experiments4 ,its properties in a liquid state are now very clearly known4 ,its boiling-point1 measured with a helium thermometer which has been compared with thermometers of oxygen and hydrogen1 is -#beb2 its critical temperature is -#bda ,c42 its critical pressure1 #ae atmospheres4 ,it is four times lighter than water1 it does not present any absorption spectrum1 and its specific heat is the greatest known4 ,it is not a conductor of electricity4 ,solidified at #ae absolute1 it is far from reminding one by its aspect of a metal2 it rather resembles a piece of perfectly pure ice1 and ,dr ,travers attributes to it a crystalline structure4 ,the last gas which has resisted liquefaction1 helium1 has recently been obtained in a liquid state2 it appears to have its boiling-point in the neighbourhood of #f absolute4#aa ,footnote #aa3 ,m4 ,poincar is here in error4 ,helium has never been liquefied4--,,ed4 #c4 ,,solids ,,and ,,liquids ,the interest of the results to which the researches on the continuity between the liquid and the gaseous states have led is so great1 that numbers of scholars have naturally been induced to inquire whether something analogous might not be found in the case of liquids and solids4 ,we might think that a similar continuity ought to be there met with1 that the universal character of the properties of matter forbade all real discontinuity between two different states1 and that1 in truth1 the solid was a prolongation of the liquid state4 ,to discover whether this supposition is correct1 it concerns us to compare the properties of liquids and solids4 ,if we find that all properties are common to the two states we have the right to believe1 even if they presented themselves in different degrees1 that1 by a continuous series of intermediary bodies1 the two classes might yet be connected4 ,if1 on the other hand1 we discover that there exists in these two classes some quality of a different nature1 we must necessarily conclude that there is a discontinuity which nothing can remove4 ,the distinction established1 from the point of view of daily custom1 between solids and liquids1 proceeds especially from the difficulty that we meet with in the one case1 and the facility in the other1 when we wish to change their form temporarily or permanently by the action of mechanical force4 ,this distinction only corresponds1 however1 in reality1 to a difference in the value of certain coefficients4 ,it is impossible to discover by this means any absolute characteristic which establishes a separation between the two classes4 ,modern researches prove this clearly4 ,it is not without use1 in order to well understand them1 to state precisely the meaning of a few terms generally rather loosely employed4 ,if a conjunction of forces acting on a homogeneous material mass happens to deform it without compressing or dilating it1 two very distinct kinds of reactions may appear which oppose themselves to the effort exercised4 ,during the time of deformation1 and during that time only1 the first make their influence felt4 ,they depend essentially on the greater or less rapidity of the deformation1 they cease with the movement1 and could not1 in any case1 bring the body back to its pristine state of equilibrium4 ,the existence of these reactions leads us to the idea of viscosity or internal friction4 ,the second kind of reactions are of a different nature4 ,they continue to act when the deformation remains stationary1 and1 if the external forces happen to disappear1 they are capable of causing the body to return to its initial form1 provided a certain limit has not been exceeded4 ,these last constitute rigidity4 ,at first sight a solid body appears to have a finite rigidity and an infinite viscosity2 a liquid1 on the contrary1 presents a certain viscosity1 but no rigidity4 ,but if we examine the matter more closely1 beginning either with the solids or with the liquids1 we see this distinction vanish4 ,tresca showed long ago that internal friction is not infinite in a solid2 certain bodies can1 so to speak1 at once flow and be moulded4 ,m4,w4 ,spring has given many examples of such phenomena4 ,on the other hand1 viscosity in liquids is never non-existent2 for were it so for water1 for example1 in the celebrated experiment effected by ,joule for the determination of the mechanical equivalent of the caloric1 the liquid borne along by the floats would slide without friction on the surrounding liquid1 and the work done by movement would be the same whether the floats did or did not plunge into the liquid mass4 ,in certain cases observed long ago with what are called pasty bodies1 this viscosity attains a value almost comparable to that observed by ,m4 ,spring in some solids4 ,nor does rigidity allow us to establish a barrier between the two states4 ,notwithstanding the extreme mobility of their particles1 liquids contain1 in fact1 vestiges of the property which we formerly wished to consider the special characteristic of solids4 ,maxwell before succeeded in rendering the existence of this rigidity very probable by examining the optical properties of a deformed layer of liquid4 ,but a ,russian physicist1 ,m4 ,schwedoff1 has gone further1 and has been able by direct experiments to show that a sheath of liquid set between two solid cylinders tends1 when one of the cylinders is subjected to a slight rotation1 to return to its original position1 and gives a measurable torsion to a thread upholding the cylinder4 ,from the knowledge of this torsion the rigidity can be deduced4 ,in the case of a solution containing #a_/b per cent4 of gelatine1 it is found that this rigidity1 enormous compared with that of water1 is still1 however1 one trillion eight hundred and forty billion times less than that of steel4 ,this figure1 exact within a few billions1 proves that the rigidity is very slight1 but exists2 and that suffices for a characteristic distinction to be founded on this property4 ,in a general way1 ,m4 ,spring has also established that we meet in solids1 in a degree more or less marked1 with the properties of liquids4 ,when they are placed in suitable conditions of pressure and time1 they flow through orifices1 transmit pressure in all directions1 diffuse and dissolve one into the other1 and react chemically on each other4 ,they may be soldered together by compression2 by the same means alloys may be produced2 and further1 which seems to clearly prove that matter in a solid state is not deprived of all molecular mobility1 it is possible to realise suitable limited reactions and equilibria between solid salts1 and these equilibria obey the fundamental laws of thermodynamics4 ,thus the definition of a solid cannot be drawn from its mechanical properties4 ,it cannot be said1 after what we have just seen1 that solid bodies retain their form1 nor that they have a limited elasticity1 for ,m4 ,spring has made known a case where the elasticity of solids is without any limit4 ,it was thought that in the case of a different phenomenon--that of crystallization--we might arrive at a clear distinction1 because here we should he dealing with a specific quality2 and that crystallized bodies would be the true solids1 amorphous bodies being at that time regarded as liquids viscous in the extreme4 ,but the studies of a ,german physicist1 ,professor ,o4 ,lehmann1 seem to prove that even this means is not infallible4 ,professor ,lehmann has succeeded1 in fact1 in obtaining with certain organic compounds-- oleate of potassium1 for instance--under certain conditions some peculiar states to which he has given the name of semi-fluid and liquid crystals4 ,these singular phenomena can only be observed and studied by means of a microscope1 and the ,carlsruhe ,professor had to devise an ingenious apparatus which enabled him to bring the preparation at the required temperature on to the very plate of the microscope4 ,it is thus made evident that these bodies act on polarized light in the manner of a crystal4 ,those that ,m4 ,lehmann terms semi-liquid still present traces of polyhedric delimitation1 but with the peaks and angles rounded by surface-tension1 while the others tend to a strictly spherical form4 ,the optical examination of the first-named bodies is very difficult1 because appearances may be produced which are due to the phenomena of refraction and imitate those of polarization4 ,for the other kind1 which are often as mobile as water1 the fact that they polarize light is absolutely unquestionable4 ,unfortunately1 all these liquids are turbid1 and it may be objected that they are not homogeneous4 ,this want of homogeneity may1 according to ,m4 ,quincke1 be due to the existence of particles suspended in a liquid in contact with another liquid miscible with it and enveloping it as might a membrane1 and the phenomena of polarization would thus be quite naturally explained4#ab ,footnote #ab3 ,professor ,quincke's last hypothesis is that all liquids on solidifying pass through a stage intermediate between solid and liquid1 in which they form what he calls foam-cells1 and assume a viscous structure resembling that of jelly4 ,see ,proc4 ,roy4 ,soc4 ,a41 #bcrd ,july #aijf4--;,,ed4 ,m4 ,tamman is of opinion that it is more a question of an emulsion1 and1 on this hypothesis1 the action on light would actually be that which has been observed4 ,various experimenters have endeavoured of recent years to elucidate this question4 ,it cannot be considered absolutely settled1 but these very curious experiments1 pursued with great patience and remarkable ingenuity1 allow us to think that there really exist certain intermediary forms between crystals and liquids in which bodies still retain a peculiar structure1 and consequently act on light1 but nevertheless possess considerable plasticity4 ,let us note that the question of the continuity of the liquid and solid states is not quite the same as the question of knowing whether there exist bodies intermediate in all respects between the solids and liquids4 ,these two problems are often wrongly confused4 ,the gap between the two classes of bodies may be filled by certain substances with intermediate properties1 such as pasty bodies and bodies liquid but still crystallized1 because they have not yet completely lost their peculiar structure4 ,yet the transition is not necessarily established in a continuous fashion when we are dealing with the passage of one and the same determinate substance from the liquid to the solid form4 ,we conceive that this change may take place by insensible degrees in the case of an amorphous body4 ,but it seems hardly possible to consider the case of a crystal1 in which molecular movements must be essentially regular1 as a natural sequence to the case of the liquid where we are1 on the contrary1 in presence of an extremely disordered state of movement4 ,m4 ,tamman has demonstrated that amorphous solids may very well1 in fact1 be regarded as superposed liquids endowed with very great viscosity4 ,but it is no longer the same thing when the solid is once in the crystallized state4 ,there is then a solution of continuity of the various properties of the substance1 and the two phases may co-exist4 ,we might presume also1 by analogy with what happens with liquids and gases1 that if we followed the curve of transformation of the crystalline into the liquid phase1 we might arrive at a kind of critical point at which the discontinuity of their properties would vanish4 ,professor ,poynting1 and after him ,professor ,planck and ,professor ,ostwald1 supposed this to be the case1 but more recently ,m4 ,tamman has shown that such a point does not exist1 and that the region of stability of the crystallized state is limited on all sides4 ,all along the curve of transformation the two states may exist in equilibrium1 but we may assert that it is impossible to realize a continuous series of intermediaries between these two states4 ,there will always be a more or less marked discontinuity in some of the properties4 ,in the course of his researches ,m4 ,tamman has been led to certain very important observations1 and has met with fresh allotropic modifications in nearly all substances1 which singularly complicate the question4 ,in the case of water1 for instance1 he finds that ordinary ice transforms itself1 under a given pressure1 at the temperature of -#hj ,c4 into another crystalline variety which is denser than water4 ,the statics of solids under high pressure is as yet1 therefore1 hardly drafted1 but it seems to promise results which will not be identical with those obtained for the statics of fluids1 though it will present at least an equal interest4 #d4 ,,the ,,deformations ,,of ,,solids ,if the mechanical properties of the bodies intermediate between solids and liquids have only lately been the object of systematic studies1 admittedly solid substances have been studied for a long time4 ,yet1 notwithstanding the abundance of researches published on elasticity by theorists and experimenters1 numerous questions with regard to them still remain in suspense4 ,we only propose to briefly indicate here a few problems recently examined1 without going into the details of questions which belong more to the domain of mechanics than to that of pure physics4 ,the deformations produced in solid bodies by increasing efforts arrange themselves in two distinct periods4 ,if the efforts are weak1 the deformations produced are also very weak and disappear when the effort ceases4 ,they are then termed elastic4 ,if the efforts exceed a certain value1 a part only of these deformations disappear1 and a part are permanent4 ,the purity of the note emitted by a sound has been often invoked as a proof of the perfect isochronism of the oscillation1 and1 consequently1 as a demonstration a posteriori of the correctness of the early law of ,hoocke governing elastic deformations4 ,this law has1 however1 during some years been frequently disputed4 ,certain mechanicians or physicists freely admit it to be incorrect1 especially as regards extremely weak deformations4 ,according to a theory in some favour1 especially in ,germany1 i4e4 the theory of ,bach1 the law which connects the elastic deformations with the efforts would be an exponential one4 ,recent experiments by ,professors ,kohlrausch and ,gruncisen1 executed under varied and precise conditions on brass1 cast iron1 slate1 and wrought iron1 do not appear to confirm ,bach's law4 ,nothing1 in point of fact1 authorises the rejection of the law of ,hoocke1 which presents itself as the most natural and most simple approximation to reality4 ,the phenomena of permanent deformation are very complex1 and it certainly seems that they cannot be explained by the older theories which insisted that the molecules only acted along the straight line which joined their centres4 ,it becomes necessary1 then1 to construct more complete hypotheses1 as the ,,mm4 ,cosserat have done in some excellent memoirs1 and we may then succeed in grouping together the facts resulting from new experiments4 ,among the experiments of which every theory must take account may be mentioned those by which ,colonel ,hartmann has placed in evidence the importance of the lines which are produced on the surface of metals when the limit of elasticity is exceeded4 ,it is to questions of the same order that the minute and patient researches of ,m4 ,bouasse have been directed4 ,this physicist1 as ingenious as he is profound1 has pursued for several years experiments on the most delicate points relating to the theory of elasticity1 and he has succeeded in defining with a precision not always attained even in the best esteemed works1 the deformations to which a body must be subjected in order to obtain comparable experiments4 ,with regard to the slight oscillations of torsion which he has specially studied1 ,m4 ,bouasse arrives at the conclusion1 in an acute discussion1 that we hardly know anything more than was proclaimed a hundred years ago by ,coulomb4 ,we see1 by this example1 that admirable as is the progress accomplished in certain regions of physics1 there still exist many over-neglected regions which remain in painful darkness4 ,the skill shown by ,m4 ,bouasse authorises us to hope that1 thanks to his researches1 a strong light will some day illumine these unknown corners4 ,a particularly interesting chapter on elasticity is that relating to the study of crystals2 and in the last few years it has been the object of remarkable researches on the part of ,m4 ,voigt4 ,these researches have permitted a few controversial questions between theorists and experimenters to be solved3 in particular1 ,m4 ,voigt has verified the consequences of the calculations1 taking care not to make1 like ,cauchy and ,poisson1 the hypothesis of central forces a mere function of distance1 and has recognized a potential which depends on the relative orientation of the molecules4 ,these considerations also apply to quasi-isotropic bodies which are1 in fact1 networks of crystals4 ,certain occasional deformations which are produced and disappear slowly may be considered as intermediate between elastic and permanent deformations4 ,of these1 the thermal deformation of glass which manifests itself by the displacement of the zero of a thermometer is an example4 ,so also the modifications which the phenomena of magnetic hysteresis or the variations of resistivity have just demonstrated4 ,many theorists have taken in hand these difficult questions4 ,m4 ,brillouin endeavours to interpret these various phenomena by the molecular hypothesis4 ,the attempt may seem bold1 since these phenomena are1 for the most part1 essentially irreversible1 and seem1 consequently1 not adaptable to mechanics4 ,but ,m4 ,brillouin makes a point of showing that1 under certain conditions1 irreversible phenomena may be created between two material points1 the actions of which depend solely on their distance2 and he furnishes striking instances which appear to prove that a great number of irreversible physical and chemical phenomena may be ascribed to the existence of states of unstable equilibria4 ,m4 ,duhem has approached the problem from another side1 and endeavours to bring it within the range of thermodynamics4 ,yet ordinary thermodynamics could not account for experimentally realizable states of equilibrium in the phenomena of viscosity and friction1 since this science declares them to be impossible4 ,m4 ,duhem1 however1 arrives at the idea that the establishment of the equations of thermodynamics presupposes1 among other hypotheses1 one which is entirely arbitrary1 namely3 that when the state of the system is given1 external actions capable of maintaining it in that state are determined without ambiguity1 by equations termed conditions of equilibrium of the system4 ,if we reject this hypothesis1 it will then be allowable to introduce into thermodynamics laws previously excluded1 and it will be possible to construct1 as ,m4 ,duhem has done1 a much more comprehensive theory4 ,the ideas of ,m4 ,duhem have been illustrated by remarkable experimental work4 ,m4 ,marchis1 for example1 guided by these ideas1 has studied the permanent modifications produced in glass by an oscillation of temperature4 ,these modifications1 which may be called phenomena of the hysteresis of dilatation1 may be followed in very appreciable fashion by means of a glass thermometer4 ,the general results are quite in accord with the previsions of ,m4 ,duhem4 ,m4 ,lenoble in researches on the traction of metallic wires1 and ,m4 ,chevalier in experiments on the permanent variations of the electrical resistance of wires of an alloy of platinum and silver when submitted to periodical variations of temperature1 have likewise afforded verifications of the theory propounded by ,m4 ,duhem4 ,in this theory1 the representative system is considered dependent on the temperature of one or several other variables1 such as1 for example1 a chemical variable4 ,a similar idea has been developed in a very fine set of memoirs on nickel steel1 by ,m4 ,ch4 ,ed4 ,guillaume4 ,the eminent physicist1 who1 by his earlier researches1 has greatly contributed to the light thrown on the analogous question of the displacement of the zero in thermometers1 concludes1 from fresh researches1 that the residual phenomena are due to chemical variations1 and that the return to the primary chemical state causes the variation to disappear4 ,he applies his ideas not only to the phenomena presented by irreversible steels1 but also to very different facts2 for example1 to phosphorescence1 certain particularities of which may be interpreted in an analogous manner4 ,nickel steels present the most curious properties1 and ,i have already pointed out the paramount importance of one of them1 hardly capable of perceptible dilatation1 for its application to metrology and chronometry4#ac ,others1 also discovered by ,m4 ,guillaume in the course of studies conducted with rare success and remarkable ingenuity1 may render great services1 because it is possible to regulate1 so to speak1 at will their mechanical or magnetic properties4 ,footnote #ac3 ,the metal known as invar4--,,ed4 ,the study of alloys in general is1 moreover1 one of those in which the introduction of the methods of physics has produced the greatest effects4 ,by the microscopic examination of a polished surface or of one indented by a reagent1 by the determination of the electromotive force of elements of which an alloy forms one of the poles1 and by the measurement of the resistivities1 the densities1 and the differences of potential or contact1 the most valuable indications as to their constitution are obtained4 ,m4 ,le ,chatelier1 ,m4 ,charpy1 ,m4 ,dumas1 ,m4 ,osmond1 in ,france2 ,sir ,w4 ,roberts ,austen and ,mr4 ,stansfield1 in ,england1 have given manifold examples of the fertility of these methods4 ,the question1 moreover1 has had a new light thrown upon it by the application of the principles of thermodynamics and of the phase rule4 ,alloys are generally known in the two states of solid and liquid4 ,fused alloys consist of one or several solutions of the component metals and of a certain number of definite combinations4 ,their composition may thus be very complex3 but ,gibbs' rule gives us at once important information on the point1 since it indicates that there cannot exist1 in general1 more than two distinct solutions in an alloy of two metals4 ,solid alloys may be classed like liquid ones4 ,two metals or more dissolve one into the other1 and form a solid solution quite analogous to the liquid solution4 ,but the study of these solid solutions is rendered singularly difficult by the fact that the equilibrium so rapidly reached in the case of liquids in this case takes days and1 in certain cases1 perhaps even centuries to become established4 ,,chapter ,v ,,solutions ,,and ,,electrolytic ,,dissociation #a4 ,,solution ,vaporization and fusion are not the only means by which the physical state of a body may be changed without modifying its chemical constitution4 ,from the most remote periods solution has also been known and studied1 but only in the last twenty years have we obtained other than empirical information regarding this phenomenon4 ,it is natural to employ here also the methods which have allowed us to penetrate into the knowledge of other transformations4 ,the problem of solution may be approached by way of thermodynamics and of the hypotheses of kinetics4 ,as long ago as #aheh1 ,kirchhoff1 by attributing to saline solutions-- that is to say1 to mixtures of water and a non-volatile liquid like sulphuric acid--the properties of internal energy1 discovered a relation between the quantity of heat given out on the addition of a certain quantity of water to a solution and the variations to which condensation and temperature subject the vapour-tension of the solution4 ,he calculated for this purpose the variations of energy which are produced when passing from one state to another by two different series of transformations2 and1 by comparing the two expressions thus obtained1 he established a relation between the various elements of the phenomenon4 ,but1 for a long time afterwards1 the question made little progress1 because there seemed to be hardly any means of introducing into this study the second principle of thermodynamics4#ad ,it was the memoir of ,gibbs which at last opened out this rich domain and enabled it to be rationally exploited4 ,as early as #ahhf1 ,m4 ,duhem showed that the theory of the thermodynamic potential furnished precise information on solutions or liquid mixtures4 ,he thus discovered over again the famous law on the lowering of the congelation temperature of solvents which had just been established by ,m4 ,raoult after a long series of now classic researches4 ,footnote #ad3 ,the second principle referred to has been thus enunciated3 ,in every engine that produces work there is a fall of temperature1 and the maximum output of a perfect engine--i4e4 the ratio between the heat consumed in work and the heat supplied--depends only on the extreme temperatures between which the fluid is evolved4--,demanet1 ,notes de ,physique ,exprimentale1 ,louvain1 #aije1 fasc4 #b1 p4 #adg4 ,clausius put it in a negative form1 as thus3 ,no engine can of itself1 without the aid of external agency1 transfer heat from a body at low temperature to a body at a high temperature4 ,cf4 ,ganot's ,physics1 #agth ,english edition1 #ejh4--;,,ed4 ,in the minds of many persons1 however1 grave doubts persisted4 ,solution appeared to be an essentially irreversible phenomenon4 ,it was therefore1 in all strictness1 impossible to calculate the entropy of a solution1 and consequently to be certain of the value of the thermodynamic potential4 ,the objection would be serious even to-day1 and1 in calculations1 what is called the paradox of ,gibbs would be an obstacle4 ,we should not hesitate1 however1 to apply the ,phase ,law to solutions1 and this law already gives us the key to a certain number of facts4 ,it puts in evidence1 for example1 the part played by the eutectic point-- that is to say1 the point at which 7to keep to the simple case in which we have to do with two bodies only1 the solvent and the solute7 the solution is in equilibrium at once with the two possible solids1 the dissolved body and the solvent solidified4 ,the knowledge of this point explains the properties of refrigerating mixtures1 and it is also one of the most useful for the theory of alloys4 ,the scruples of physicists ought to have been removed on the memorable occasion when ,professor ,van t',hoff demonstrated that solution can operate reversibly by reason of the phenomena of osmosis4 ,but the experiment can only succeed in very rare cases2 and1 on the other hand1 ,professor ,van t',hoff was naturally led to another very bold conception4 ,he regarded the molecule of the dissolved body as a gaseous one1 and assimilated solution1 not as had hitherto been the rule1 to fusion1 but to a kind of vaporization4 ,naturally his ideas were not immediately accepted by the scholars most closely identified with the classic tradition4 ,it may perhaps not be without use to examine here the principles of ,professor ,van t',hoff's theory4 #b4 ,,osmosis ,osmosis1 or diffusion through a septum1 is a phenomenon which has been known for some time4 ,the discovery of it is attributed to the ,abb ,nollet1 who is supposed to have observed it in #agdh1 during some researches on liquids in ebullition4 ,a classic experiment by ,dutrochet1 effected about #ahcj1 makes this phenomenon clear4 ,into pure water is plunged the lower part of a vertical tube containing pure alcohol1 open at the top and closed at the bottom by a membrane1 such as a pig's bladder1 without any visible perforation4 ,in a very short time it will be found1 by means of an areometer for instance1 that the water outside contains alcohol1 while the alcohol of the tube1 pure at first1 is now diluted4 ,two currents have therefore passed through the membrane1 one of water from the outside to the inside1 and one of alcohol in the converse direction4 ,it is also noted that a difference in the levels has occurred1 and that the liquid in the tube now rises to a considerable height4 ,it must therefore be admitted that the flow of the water has been more rapid than that of the alcohol4 ,at the commencement1 the water must have penetrated into the tube much more rapidly than the alcohol left it4 ,hence the difference in the levels1 and1 consequently1 a difference of pressure on the two faces of the membrane4 ,this difference goes on increasing1 reaches a maximum1 then diminishes1 and vanishes when the diffusion is complete1 final equilibrium being then attained4 ,the phenomenon is evidently connected with diffusion4 ,if water is very carefully poured on to alcohol1 the two layers1 separate at first1 mingle by degrees till a homogeneous substance is obtained4 ,the bladder seems not to have prevented this diffusion from taking place1 but it seems to have shown itself more permeable to water than to alcohol4 ,may it not therefore be supposed that there must exist dividing walls in which this difference of permeability becomes greater and greater1 which would be permeable to the solvent and absolutely impermeable to the solute8 ,if this be so1 the phenomena of these semi-permeable walls1 as they are termed1 can be observed in particularly simple conditions4 ,the answer to this question has been furnished by biologists1 at which we cannot be surprised4 ,the phenomena of osmosis are naturally of the first importance in the action of organisms1 and for a long time have attracted the attention of naturalists4 ,de ,vries imagined that the contractions noticed in the protoplasm of cells placed in saline solutions were due to a phenomenon of osmosis1 and1 upon examining more closely certain peculiarities of cell life1 various scholars have demonstrated that living cells are enclosed in membranes permeable to certain substances and entirely impermeable to others4 ,it was interesting to try to reproduce artificially semi-permeable walls analogous to those thus met with in nature2#ae and ,traube and ,pfeffer seem to have succeeded in one particular case4 ,traube has pointed out that the very delicate membrane of ferrocyanide of potassium which is obtained with some difficulty by exposing it to the reaction of sulphate of copper1 is permeable to water1 but will not permit the passage of the majority of salts4 ,pfeffer1 by producing these walls in the interstices of a porous porcelain1 has succeeded in giving them sufficient rigidity to allow measurements to be made4 ,it must be allowed that1 unfortunately1 no physicist or chemist has been as lucky as these two botanists2 and the attempts to reproduce semi-permeable walls completely answering to the definition1 have never given but mediocre results4 ,if1 however1 the experimental difficulty has not been overcome in an entirely satisfactory manner1 it at least appears very probable that such walls may nevertheless exist4#af ,footnote #ae3 ,see next note4--,,ed4 ,footnote #af3 ,m4 ,stephane ,leduc1 ,professor of ,biology of ,nantes1 has made many experiments in this connection1 and the artificial cells exhibited by him to the ,association franaise pour l'avancement des ,sciences1 at their meeting at ,grenoble in #aijd and reproduced in their ,actes1 are particularly noteworthy4--,,ed4 ,nevertheless1 in the case of gases1 there exists an excellent example of a semi-permeable wall1 and a partition of platinum brought to a higher than red heat is1 as shown by ,m4 ,villard in some ingenious experiments1 completely impermeable to air1 and very permeable1 on the contrary1 to hydrogen4 ,it can also be experimentally demonstrated that on taking two recipients separated by such a partition1 and both containing nitrogen mixed with varying proportions of hydrogen1 the last-named gas will pass through the partition in such a way that the concentration--that is to say1 the mass of gas per unit of volume-- will become the same on both sides4 ,only then will equilibrium be established2 and1 at that moment1 an excess of pressure will naturally be produced in that recipient which1 at the commencement1 contained the gas with the smallest quantity of hydrogen4 ,this experiment enables us to anticipate what will happen in a liquid medium with semi-permeable partitions4 ,between two recipients1 one containing pure water1 the other1 say1 water with sugar in solution1 separated by one of these partitions1 there will be produced merely a movement of the pure towards the sugared water1 and following this1 an increase of pressure on the side of the last4 ,but this increase will not be without limits4 ,at a certain moment the pressure will cease to increase and will remain at a fixed value which now has a given direction4 ,this is the osmotic pressure4 ,pfeffer demonstrated that1 for the same substance1 the osmotic pressure is proportional to the concentration1 and consequently in inverse ratio to the volume occupied by a similar mass of the solute4 ,he gave figures from which it was easy1 as ,professor ,van t',hoff found1 to draw the conclusion that1 in a constant volume1 the osmotic pressure is proportional to the absolute temperature4 ,de ,vries1 moreover1 by his remarks on living cells1 extended the results which ,pfeffer had applied to one case only--that is1 to the one that he had been able to examine experimentally4 ,such are the essential facts of osmosis4 ,we may seek to interpret them and to thoroughly examine the mechanism of the phenomenon2 but it must be acknowledged that as regards this point1 physicists are not entirely in accord4 ,in the opinion of ,professor ,nernst1 the permeability of semi-permeable membranes is simply due to differences of solubility in one of the substances of the membrane itself4 ,other physicists think it attributable1 either to the difference in the dimensions of the molecules1 of which some might pass through the pores of the membrane and others be stopped by their relative size1 or to these molecules' greater or less mobility4 ,for others1 again1 it is the capillary phenomena which here act a preponderating part4 ,this last idea is already an old one3 ,jager1 ,more1 and ,professor ,traube have all endeavoured to show that the direction and speed of osmosis are determined by differences in the surface-tensions2 and recent experiments1 especially those of ,batelli1 seem to prove that osmosis establishes itself in the way which best equalizes the surface-tensions of the liquids on both sides of the partition4 ,solutions possessing the same surface-tension1 though not in molecular equilibrium1 would thus be always in osmotic equilibrium4 ,we must not conceal from ourselves that this result would be in contradiction with the kinetic theory4 #c4 ,,application ,,to ,,the ,,theory ,,of ,,solution ,if there really exist partitions permeable to one body and impermeable to another1 it may be imagined that the homogeneous mixture of these two bodies might be effected in the converse way4 ,it can be easily conceived1 in fact1 that by the aid of osmotic pressure it would be possible1 for example1 to dilute or concentrate a solution by driving through the partition in one direction or another a certain quantity of the solvent by means of a pressure kept equal to the osmotic pressure4 ,this is the important fact which ,professor ,van t' ,hoff perceived4 ,the existence of such a wall in all possible cases evidently remains only a very legitimate hypothesis1--a fact which ought not to be concealed4 ,relying solely on this postulate1 ,professor ,van t' ,hoff easily established1 by the most correct method1 certain properties of the solutions of gases in a volatile liquid1 or of non-volatile bodies in a volatile liquid4 ,to state precisely the other relations1 we must admit1 in addition1 the experimental laws discovered by ,pfeffer4 ,but without any hypothesis it becomes possible to demonstrate the laws of ,raoult on the lowering of the vapour-tension and of the freezing point of solutions1 and also the ratio which connects the heat of fusion with this decrease4 ,these considerable results can evidently be invoked as a posteriori proofs of the exactitude of the experimental laws of osmosis4 ,they are not1 however1 the only ones that ,professor ,van t' ,hoff has obtained by the same method4 ,this illustrious scholar was thus able to find anew ,guldberg and ,waage's law on chemical equilibrium at a constant temperature1 and to show how the position of the equilibrium changes when the temperature happens to change4 ,if now we state1 in conformity with the laws of ,pfeffer1 that the product of the osmotic pressure by the volume of the solution is equal to the absolute temperature multiplied by a coefficient1 and then look for the numerical figure of this latter in a solution of sugar1 for instance1 we find that this value is the same as that of the analogous coefficient of the characteristic equation of a perfect gas4 ,there is in this a coincidence which has also been utilized in the preceding thermodynamic calculations4 ,it may be purely fortuitous1 but we can hardly refrain from finding in it a physical meaning4 ,professor ,van t',hoff has considered this coincidence a demonstration that there exists a strong analogy between a body in solution and a gas2 as a matter of fact1 it may seem that1 in a solution1 the distance between the molecules becomes comparable to the molecular distances met with in gases1 and that the molecule acquires the same degree of liberty and the same simplicity in both phenomena4 ,in that case it seems probable that solutions will be subject to laws independent of the chemical nature of the dissolved molecule and comparable to the laws governing gases1 while if we adopt the kinetic image for the gas1 we shall be led to represent to ourselves in a similar way the phenomena which manifest themselves in a solution4 ,osmotic pressure will then appear to be due to the shock of the dissolved molecules against the membrane4 ,it will come from one side of this partition to superpose itself on the hydrostatic pressure1 which latter must have the same value on both sides4 ,the analogy with a perfect gas naturally becomes much greater as the solution becomes more diluted4 ,it then imitates gas in some other properties2 the internal work of the variation of volume is nil1 and the specific heat is only a function of the temperature4 ,a solution which is diluted by a reversible method is cooled like a gas which expands adiabatically4#ag ,footnote #ag3 ,that is1 without receiving or emitting any heat4--,,ed4 ,it must1 however1 be acknowledged that1 in other points1 the analogy is much less perfect4 ,the opinion which sees in solution a phenomenon resembling fusion1 and which has left an indelible trace in everyday language 7we shall always say3 to melt sugar in water7 is certainly not without foundation4 ,certain of the reasons which might be invoked to uphold this opinion are too evident to be repeated here1 though others more recondite might be quoted4 ,the fact that the internal energy generally becomes independent of the concentration when the dilution reaches even a moderately high value is rather in favour of the hypothesis of fusion4 ,we must not forget1 however1 the continuity of the liquid and gaseous states2 and we may consider it in an absolute way a question devoid of sense to ask whether in a solution the solute is in the liquid or the gaseous state4 ,it is in the fluid state1 and perhaps in conditions opposed to those of a body in the state of a perfect gas4 ,it is known1 of course1 that in this case the manometrical pressure must be regarded as very great in relation to the internal pressure which1 in the characteristic equation1 is added to the other4 ,may it not seem possible that in the solution it is1 on the contrary1 the internal pressure which is dominant1 the manometric pressure becoming of no account8 ,the coincidence of the formulas would thus be verified1 for all the characteristic equations are symmetrical with regard to these two pressures4 ,from this point of view the osmotic pressure would be considered as the result of an attraction between the solvent and the solute2 and it would represent the difference between the internal pressures of the solution and of the pure solvent4 ,these hypotheses are highly interesting1 and very suggestive2 but from the way in which the facts have been set forth1 it will appear1 no doubt1 that there is no obligation to admit them in order to believe in the legitimacy of the application of thermodynamics to the phenomena of solution4 #d4 ,,electrolytic ,,dissociation ,from the outset ,professor ,van t' ,hoff was brought to acknowledge that a great number of solutions formed very notable exceptions which were very irregular in appearance4 ,the analogy with gases did not seem to be maintained1 for the osmotic pressure had a very different value from that indicated by the theory4 ,everything1 however1 came right if one multiplied by a factor1 determined according to each case1 but greater than unity1 the constant of the characteristic formula4 ,similar divergences were manifested in the delays observed in congelation1 and disappeared when subjected to an analogous correction4 ,thus the freezing-point of a normal solution1 containing a molecule gramme 7that is1 the number of grammes equal to the figure representing the molecular mass7 of alcohol or sugar in water1 falls #a4he ,c4 ,if the laws of solution were identically the same for a solution of sea-salt1 the same depression should be noticed in a saline solution also containing #a molecule per litre4 ,in fact1 the fall reaches #c4bf1 and the solution behaves as if it contained1 not #a1 but #a4ge normal molecules per litre4 ,the consideration of the osmotic pressures would lead to similar observations1 but we know that the experiment would be more difficult and less precise4 ,we may wonder whether anything really analogous to this can be met with in the case of a gas1 and we are thus led to consider the phenomena of dissociation4#ah ,if we heat a body which1 in a gaseous state1 is capable of dissociation--hydriodic acid1 for example--at a given temperature1 an equilibrium is established between three gaseous bodies1 the acid1 the iodine1 and the hydrogen4 ,the total mass will follow with fair closeness ,mariotte's law1 but the characteristic constant will no longer be the same as in the case of a non-dissociated gas4 ,we here no longer have to do with a single molecule1 since each molecule is in part dissociated4 ,footnote #ah3 ,dissociation must be distinguished from decomposition1 which is what occurs when the whole of a particle 7compound1 molecule1 atom1 etc47 breaks up into its component parts4 ,in dissociation the breaking up is only partial1 and the resultant consists of a mixture of decomposed and undecomposed parts4 ,see ,ganot's ,physics1 #agth ,english edition1 #cie1 for examples4--,,ed4 ,the comparison of the two cases leads to the employment of a new image for representing the phenomenon which has been produced throughout the saline solution4 ,we have introduced a single molecule of salt1 and everything occurs as if there were #a4ge molecules4 ,may it not really be said that the number is #a4ge1 because the sea-salt is partly dissociated1 and a molecule has become transformed into #j4ge molecule of sodium1 #j4ge of chlorium1 and #j4be of salt8 ,this is a way of speaking which seems1 at first sight1 strangely contradicted by experiment4 ,professor ,van t' ,hoff1 like other chemists1 would certainly have rejected--in fact1 he did so at first-- such a conception1 if1 about the same time1 an illustrious ,swedish scholar1 ,m4 ,arrhenius1 had not been brought to the same idea by another road1 and1 had not by stating it precisely and modifying it1 presented it in an acceptable form4 ,a brief examination will easily show that all the substances which are exceptions to the laws of ,van t',hoff are precisely those which are capable of conducting electricity when undergoing decomposition--that is to say1 are electrolytes4 ,the coincidence is absolute1 and cannot be simply due to chance4 ,now1 the phenomena of electrolysis have1 for a long time1 forced upon us an almost necessary image4 ,the saline molecule is always decomposed1 as we know1 in the primary phenomenon of electrolysis into two elements which ,faraday termed ions4 ,secondary reactions1 no doubt1 often come to complicate the question1 but these are chemical reactions belonging to the general order of things1 and have nothing to do with the electric action working on the solution4 ,the simple phenomenon is always the same--decomposition into two ions1 followed by the appearance of one of these ions at the positive and of the other at the negative electrode4 ,but as the very slightest expenditure of energy is sufficient to produce the commencement of electrolysis1 it is necessary to suppose that these two ions are not united by any force4 ,thus the two ions are1 in a way1 dissociated4 ,clausius1 who was the first to represent the phenomena by this symbol1 supposed1 in order not to shock the feelings of chemists too much1 that this dissociation only affected an infinitesimal fraction of the total number of the molecules of the salt1 and thereby escaped all check4 ,this concession was unfortunate1 and the hypothesis thus lost the greater part of its usefulness4 ,m4 ,arrhenius was bolder1 and frankly recognized that dissociation occurs at once in the case of a great number of molecules1 and tends to increase more and more as the solution becomes more dilute4 ,it follows the comparison with a gas which1 while partially dissociated in an enclosed space1 becomes wholly so in an infinite one4 ,m4 ,arrhenius was led to adopt this hypothesis by the examination of experimental results relating to the conductivity of electrolytes4 ,in order to interpret certain facts1 it has to be recognized that a part only of the molecules in a saline solution can be considered as conductors of electricity1 and that by adding water the number of molecular conductors is increased4 ,this increase1 too1 though rapid at first1 soon becomes slower1 and approaches a certain limit which an infinite dilution would enable it to attain4 ,if the conducting molecules are the dissociated molecules1 then the dissociation 7so long as it is a question of strong acids and salts7 tends to become complete in the case of an unlimited dilution4 ,the opposition of a large number of chemists and physicists to the ideas of ,m4 ,arrhenius was at first very fierce4 ,it must be noted with regret that1 in ,france particularly1 recourse was had to an arm which scholars often wield rather clumsily4 ,they joked about these free ions in solution1 and they asked to see this chlorine and this sodium which swam about the water in a state of liberty4 ,but in science1 as elsewhere1 irony is not argument1 and it soon had to be acknowledged that the hypothesis of ,m4 ,arrhenius showed itself singularly fertile and had to be regarded1 at all events1 as a very expressive image1 if not1 indeed1 entirely in conformity with reality4 ,it would certainly be contrary to all experience1 and even to common sense itself1 to suppose that in dissolved chloride of sodium there is really free sodium1 if we suppose these atoms of sodium to be absolutely identical with ordinary atoms4 ,but there is a great difference4 ,in the one case the atoms are electrified1 and carry a relatively considerable positive charge1 inseparable from their state as ions1 while in the other they are in the neutral state4 ,we may suppose that the presence of this charge brings about modifications as extensive as one pleases in the chemical properties of the atom4 ,thus the hypothesis will be removed from all discussion of a chemical order1 since it will have been made plastic enough beforehand to adapt itself to all the known facts2 and if we object that sodium cannot subsist in water because it instantaneously decomposes the latter1 the answer is simply that the sodium ion does not decompose water as does ordinary sodium4 ,still1 other objections might be raised which could not be so easily refuted4 ,one1 to which chemists not unreasonably attached great importance1 was this3--,if a certain quantity of chloride of sodium is dissociated into chlorine and sodium1 it should be possible1 by diffusion1 for example1 which brings out plainly the phenomena of dissociation in gases1 to extract from the solution a part either of the chlorine or of the sodium1 while the corresponding part of the other compound would remain4 ,this result would be in flagrant contradiction with the fact that1 everywhere and always1 a solution of salt contains strictly the same proportions of its component elements4 ,m4 ,arrhenius answers to this that the electrical forces in ordinary conditions prevent separation by diffusion or by any other process4 ,professor ,nernst goes further1 and has shown that the concentration currents which are produced when two electrodes of the same substance are plunged into two unequally concentrated solutions may be interpreted by the hypothesis that1 in these particular conditions1 the diffusion does bring about a separation of the ions4 ,thus the argument is turned round1 and the proof supposed to be given of the incorrectness of the theory becomes a further reason in its favour4 ,it is possible1 no doubt1 to adduce a few other experiments which are not very favourable to ,m4 ,arrhenius's point of view1 but they are isolated cases2 and1 on the whole1 his theory has enabled many isolated facts1 till then scattered1 to be co-ordinated1 and has allowed very varied phenomena to be linked together4 ,it has also suggested--and1 moreover1 still daily suggests--researches of the highest order4 ,in the first place1 the theory of ,arrhenius explains electrolysis very simply4 ,the ions which1 so to speak1 wander about haphazard1 and are uniformly distributed throughout the liquid1 steer a regular course as soon as we dip in the trough containing the electrolyte the two electrodes connected with the poles of the dynamo or generator of electricity4 ,then the charged positive ions travel in the direction of the electromotive force and the negative ions in the opposite direction4 ,on reaching the electrodes they yield up to them the charges they carry1 and thus pass from the state of ion into that of ordinary atom4 ,moreover1 for the solution to remain in equilibrium1 the vanished ions must be immediately replaced by others1 and thus the state of ionisation of the electrolyte remains constant and its conductivity persists4 ,all the peculiarities of electrolysis are capable of interpretation3 the phenomena of the transport of ions1 the fine experiments of ,m4 ,bouty1 those of ,professor ,kohlrausch and of ,professor ,ostwald on various points in electrolytic conduction1 all support the theory4 ,the verifications of it can even be quantitative1 and we can foresee numerical relations between conductivity and other phenomena4 ,the measurement of the conductivity permits the number of molecules dissociated in a given solution to be calculated1 and the number is thus found to be precisely the same as that arrived at if it is wished to remove the disagreement between reality and the anticipations which result from the theory of ,professor ,van t' ,hoff4 ,the laws of cryoscopy1 of tonometry1 and of osmosis thus again become strict1 and no exception to them remains4 ,if the dissociation of salts is a reality and is complete in a dilute solution1 any of the properties of a saline solution whatever should be represented numerically as the sum of three values1 of which one concerns the positive ion1 a second the negative ion1 and the third the solvent4 ,the properties of the solutions would then be what are called additive properties4 ,numerous verifications may be attempted by very different roads4 ,they generally succeed very well2 and whether we measure the electric conductivity1 the density1 the specific heats1 the index of refraction1 the power of rotatory polarization1 the colour1 or the absorption spectrum1 the additive property will everywhere be found in the solution4 ,the hypothesis1 so contested at the outset by the chemists1 is1 moreover1 assuring its triumph by important conquests in the domain of chemistry itself4 ,it permits us to give a vivid explanation of chemical reaction1 and for the old motto of the chemists1 ,corpora non agunt1 nisi soluta1 it substitutes a modern one1 ,it is especially the ions which react4 ,thus1 for example1 all salts of iron1 which contain iron in the state of ions1 give similar reactions2 but salts such as ferrocyanide of potassium1 in which iron does not play the part of an ion1 never give the characteristic reactions of iron4 ,professor ,ostwald and his pupils have drawn from the hypothesis of ,arrhenius manifold consequences which have been the cause of considerable progress in physical chemistry4 ,professor ,ostwald has shown1 in particular1 how this hypothesis permits the quantitative calculation of the conditions of equilibrium of electrolytes and solutions1 and especially of the phenomena of neutralization4 ,if a dissolved salt is partly dissociated into ions1 this solution must be limited by an equilibrium between the non-dissociated molecule and the two ions resulting from the dissociation2 and1 assimilating the phenomenon to the case of gases1 we may take for its study the laws of ,gibbs and of ,guldberg and ,waage4 ,the results are generally very satisfactory1 and new researches daily furnish new checks4 ,professor ,nernst1 who before gave1 as has been said1 a remarkable interpretation of the diffusion of electrolytes1 has1 in the direction pointed out by ,m4 ,arrhenius1 developed a theory of the entire phenomena of electrolysis1 which1 in particular1 furnishes a striking explanation of the mechanism of the production of electromotive force in galvanic batteries4 ,extending the analogy1 already so happily invoked1 between the phenomena met with in solutions and those produced in gases1 ,professor ,nernst supposes that metals tend1 as it were1 to vaporize when in presence of a liquid4 ,a piece of zinc introduced1 for example1 into pure water gives birth to a few metallic ions4 ,these ions become positively charged1 while the metal naturally takes an equal charge1 but of contrary sign4 ,thus the solution and the metal are both electrified2 but this sort of vaporization is hindered by electrostatic attraction1 and as the charges borne by the ions are considerable1 an equilibrium will be established1 although the number of ions which enter the solution will be very small4 ,if the liquid1 instead of being a solvent like pure water1 contains an electrolyte1 it already contains metallic ions1 the osmotic pressure of which will be opposite to that of the solution4 ,three cases may then present themselves--either there will be equilibrium1 or the electrostatic attraction will oppose itself to the pressure of solution and the metal will be negatively charged1 or1 finally1 the attraction will act in the same direction as the pressure1 and the metal will become positively and the solution negatively charged4 ,developing this idea1 ,professor ,nernst calculates1 by means of the action of the osmotic pressures1 the variations of energy brought into play and the value of the differences of potential by the contact of the electrodes and electrolytes4 ,he deduces this from the electromotive force of a single battery cell which becomes thus connected with the values of the osmotic pressures1 or1 if you will1 thanks to the relation discovered by ,van t' ,hoff1 with the concentrations4 ,some particularly interesting electrical phenomena thus become connected with an already very important group1 and a new bridge is built which unites two regions long considered foreign to each other4 ,the recent discoveries on the phenomena produced in gases when rendered conductors of electricity almost force upon us1 as we shall see1 the idea that there exist in these gases electrified centres moving through the field1 and this idea gives still greater probability to the analogous theory explaining the mechanism of the conductivity of liquids4 ,it will also be useful1 in order to avoid confusion1 to restate with precision this notion of electrolytic ions1 and to ascertain their magnitude1 charge1 and velocity4 ,the two classic laws of ,faraday will supply us with important information4 ,the first indicates that the quantity of electricity passing through the liquid is proportional to the quantity of matter deposited on the electrodes4 ,this leads us at once to the consideration that1 in any given solution1 all the ions possess individual charges equal in absolute value4 ,the second law may be stated in these terms3 an atom-gramme of metal carries with it into electrolysis a quantity of electricity proportionate to its valency4#ai ,footnote #ai3 ,the valency or atomicity of an element may be defined as the power it possesses of entering into compounds in a certain fixed proportion4 ,as hydrogen is generally taken as the standard1 in practice the valency of an atom is the number of hydrogen atoms it will combine with or replace4 ,thus chlorine and the rest of the halogens1 the atoms of which combine with one atom of hydrogen1 are called univalent1 oxygen a bivalent element1 and so on4--,,ed4 ,numerous experiments have made known the total mass of hydrogen capable of carrying one coulomb1 and it will therefore be possible to estimate the charge of an ion of hydrogen if the number of atoms of hydrogen in a given mass be known4 ,this last figure is already furnished by considerations derived from the kinetic theory1 and agrees with the one which can be deduced from the study of various phenomena4 ,the result is that an ion of hydrogen having a mass of #a4c x #aj-bj grammes bears a charge of #a4c ,x #aj-bj electromagnetic units2 and the second law will immediately enable the charge of any other ion to be similarly estimated4 ,the measurements of conductivity1 joined to certain considerations relating to the differences of concentration which appear round the electrode in electrolysis1 allow the speed of the ions to be calculated4 ,thus1 in a liquid containing #a_/ajth of a hydrogen-ion per litre1 the absolute speed of an ion would be #c_/ajths of a millimetre per second in a field where the fall of potential would be #a volt per centimetre4 ,sir ,oliver ,lodge1 who has made direct experiments to measure this speed1 has obtained a figure very approximate to this4 ,this value is very small compared to that which we shall meet with in gases4 ,another consequence of the laws of ,faraday1 to which1 as early as #ahha1 ,helmholtz drew attention1 may be considered as the starting-point of certain new doctrines we shall come across later4 ,helmholtz says3 ,if we accept the hypothesis that simple bodies are composed of atoms1 we are obliged to admit that1 in the same way1 electricity1 whether positive or negative1 is composed of elementary parts which behave like atoms of electricity4 ,the second law seems1 in fact1 analogous to the law of multiple proportions in chemistry1 and it shows us that the quantities of electricity carried vary from the simple to the double or treble1 according as it is a question of a uni-1 bi-1 or trivalent metal2 and as the chemical law leads up to the conception of the material atom1 so does the electrolytic law suggest the idea of an electric atom4 ,,chapter ,,vi ,,the ,,ether #a4 ,,the ,,luminiferous ,,ether ,it is in the works of ,descartes that we find the first idea of attributing those physical phenomena which the properties of matter fail to explain to some subtle matter which is the receptacle of the energy of the universe4 ,in our times this idea has had extraordinary luck4 ,after having been eclipsed for two hundred years by the success of the immortal synthesis of ,newton1 it gained an entirely new splendour with ,fresnel and his followers4 ,thanks to their admirable discoveries1 the first stage seemed accomplished1 the laws of optics were represented by a single hypothesis1 marvellously fitted to allow us to anticipate unknown phenomena1 and all these anticipations were subsequently fully verified by experiment4 ,but the researches of ,faraday1 ,maxwell1 and ,hertz authorized still greater ambitions2 and it really seemed that this medium1 to which it was agreed to give the ancient name of ether1 and which had already explained light and radiant heat1 would also be sufficient to explain electricity4 ,thus the hope began to take form that we might succeed in demonstrating the unity of all physical forces4 ,it was thought that the knowledge of the laws relating to the inmost movements of this ether might give us the key to all phenomena1 and might make us acquainted with the method in which energy is stored up1 transmitted1 and parcelled out in its external manifestations4 ,we cannot study here all the problems which are connected with the physics of the ether4 ,to do this a complete treatise on optics would have to be written and a very lengthy one on electricity4 ,i shall simply endeavour to show rapidly how in the last few years the ideas relative to the constitution of this ether have evolved1 and we shall see if it be possible without self-delusion to imagine that a single medium can really allow us to group all the known facts in one comprehensive arrangement4 ,as constructed by ,fresnel1 the hypothesis of the luminous ether1 which had so great a struggle at the outset to overcome the stubborn resistance of the partisans of the then classic theory of emission1 seemed1 on the contrary1 to possess in the sequel an unshakable strength4 ,lam1 though a prudent mathematician1 wrote3 ,the existence of the ethereal fluid is incontestably demonstrated by the propagation of light through the planetary spaces1 and by the explanation1 so simple and so complete1 of the phenomena of diffraction in the wave theory of light2 and he adds3 ,the laws of double refraction prove with no less certainty that the ether exists in all diaphanous media4 ,thus the ether was no longer an hypothesis1 but in some sort a tangible reality4 ,but the ethereal fluid of which the existence was thus proclaimed has some singular properties4 ,were it only a question of explaining rectilinear propagation1 reflexion1 refraction1 diffraction1 and interferences notwithstanding grave difficulties at the outset and the objections formulated by ,laplace and ,poisson 7some of which1 though treated somewhat lightly at the present day1 have not lost all value71 we should be under no obligation to make any hypothesis other than that of the undulations of an elastic medium1 without deciding in advance anything as to the nature and direction of the vibrations4 ,this medium would1 naturally--since it exists in what we call the void--be considered as imponderable4 ,it may be compared to a fluid of negligible mass--since it offers no appreciable resistance to the motion of the planets--but is endowed with an enormous elasticity1 because the velocity of the propagation of light is considerable4 ,it must be capable of penetrating into all transparent bodies1 and of retaining there1 so to speak1 a constant elasticity1 but must there become condensed1 since the speed of propagation in these bodies is less than in a vacuum4 ,such properties belong to no material gas1 even the most rarefied1 but they admit of no essential contradiction1 and that is the important point4#bj ,footnote #bj3 ,since this was written1 however1 men of science have become less unanimous than they formerly were on this point4 ,the veteran chemist ,professor ,mendeleff has given reasons for thinking that the ether is an inert gas with an atomic weight a million times less than that of hydrogen1 and a velocity of #bbej kilometres per second 7,principles of ,chemistry1 ,eng4 ed41 #aije1 vol4 ii4 p4 #ebf74 ,on the other hand1 the well-known physicist ,dr ,a4,h4 ,bucherer1 speaking at the ,naturforscherversammlung1 held at ,stuttgart in #aijf1 declared his disbelief in the existence of the ether1 which he thought could not be reconciled at once with the ,maxwellian theory and the known facts4--,,ed4 ,it was the study of the phenomena of polarization which led ,fresnel to his bold conception of transverse vibrations1 and subsequently induced him to penetrate further into the constitution of the ether4 ,we know the experiment of ,arago on the noninterference of polarized rays in rectangular planes4 ,while two systems of waves1 proceeding from the same source of natural light and propagating themselves in nearly parallel directions1 increase or become destroyed according to whether the nature of the superposed waves are of the same or of contrary signs1 the waves of the rays polarized in perpendicular planes1 on the other hand1 can never interfere with each other4 ,whatever the difference of their course1 the intensity of the light is always the sum of the intensity of the two rays4 ,fresnel perceived that this experiment absolutely compels us to reject the hypothesis of longitudinal vibrations acting along the line of propagation in the direction of the rays4 ,to explain it1 it must of necessity be admitted1 on the contrary1 that the vibrations are transverse and perpendicular to the ray4 ,verdet could say1 in all truth1 ,it is not possible to deny the transverse direction of luminous vibrations1 without at the same time denying that light consists of an undulatory movement4 ,such vibrations do not and cannot exist in any medium resembling a fluid4 ,the characteristic of a fluid is that its different parts can displace themselves with regard to one another without any reaction appearing so long as a variation of volume is not produced4 ,there certainly may exist1 as we have seen1 certain traces of rigidity in a liquid1 but we cannot conceive such a thing in a body infinitely more subtle than rarefied gas4 ,among material bodies1 a solid alone really possesses the rigidity sufficient for the production within it of transverse vibrations and for their maintenance during their propagation4 ,since we have to attribute such a property to the ether1 we may add that on this point it resembles a solid1 and ,lord ,kelvin has shown that this solid1 would be much more rigid than steel4 ,this conclusion produces great surprise in all who hear it for the first time1 and it is not rare to hear it appealed to as an argument against the actual existence of the ether4 ,it does not seem1 however1 that such an argument can be decisive4 ,there is no reason for supposing that the ether ought to be a sort of extension of the bodies we are accustomed to handle4 ,its properties may astonish our ordinary way of thinking1 but this rather unscientific astonishment is not a reason for doubting its existence4 ,real difficulties would appear only if we were led to attribute to the ether1 not singular properties which are seldom found united in the same substance1 but properties logically contradictory4 ,in short1 however odd such a medium may appear to us1 it cannot be said that there is any absolute incompatibility between its attributes4 ,it would even be possible1 if we wished1 to suggest images capable of representing these contrary appearances4 ,various authors have done so4 ,thus1 ,m4 ,boussinesq assumes that the ether behaves like a very rarefied gas in respect of the celestial bodies1 because these last move1 while bathed in it1 in all directions and relatively slowly1 while they permit it to retain1 so to speak1 its perfect homogeneity4 ,on the other hand1 its own undulations are so rapid that so far as they are concerned the conditions become very different1 and its fluidity has1 one might say1 no longer the time to come in4 ,hence its rigidity alone appears4 ,another consequence1 very important in principle1 of the fact that vibrations of light are transverse1 has been well put in evidence by ,fresnel4 ,he showed how we have1 in order to understand the action which excites without condensation the sliding of successive layers of the ether during the propagation of a vibration1 to consider the vibrating medium as being composed of molecules separated by finite distances4 ,certain authors1 it is true1 have proposed theories in which the action at a distance of these molecules are replaced by actions of contact between parallelepipeds sliding over one another2 but1 at bottom1 these two points of view both lead us to conceive the ether as a discontinuous medium1 like matter itself4 ,the ideas gathered from the most recent experiments also bring us to the same conclusion4 #b4 ,,radiations ,in the ether thus constituted there are therefore propagated transverse vibrations1 regarding which all experiments in optics furnish very precise information4 ,the amplitude of these vibrations is exceedingly small1 even in relation to the wave-length1 small as these last are4 ,if1 in fact1 the amplitude of the vibrations acquired a noticeable value in comparison with the wave-length1 the speed of propagation should increase with the amplitude4 ,yet1 in spite of some curious experiments which seem to establish that the speed of light does alter a little with its intensity1 we have reason to believe that1 as regards light1 the amplitude of the oscillations in relation to the wave-length is incomparably less than in the case of sound4 ,it has become the custom to characterise each vibration by the path which the vibratory movement traverses during the space of a vibration--by the length of wave1 in a word--rather than by the duration of the vibration itself4 ,to measure wave-lengths1 the methods must be employed to which ,i have already alluded on the subject of measurements of length4 ,professor ,michelson1 on the one hand1 and ,,mm4 ,perot and ,fabry1 on the other1 have devised exceedingly ingenious processes1 which have led to results of really unhoped-for precision4 ,the very exact knowledge also of the speed of the propagation of light allows the duration of a vibration to be calculated when once the wave-length is known4 ,it is thus found that1 in the case of visible light1 the number of the vibrations from the end of the violet to the infra-red varies from four hundred to two hundred billions per second4 ,this gamut is not1 however1 the only one the ether can give4 ,for a long time we have known ultra-violet radiations still more rapid1 and1 on the other hand1 infra-red ones more slow1 while in the last few years the field of known radiations has been singularly extended in both directions4 ,it is to ,m4 ,rubens and his fellow-workers that are due the most brilliant conquests in the matter of great wave-lengths4 ,he had remarked that1 in their study1 the difficulty of research proceeds from the fact that the extreme waves of the infra-red spectrum only contain a small part of the total energy emitted by an incandescent body2 so that if1 for the purpose of study1 they are further dispersed by a prism or a grating1 the intensity at any one point becomes so slight as to be no longer observable4 ,his original idea was to obtain1 without prism or grating1 a homogeneous pencil of great wave-length sufficiently intense to be examined4 ,for this purpose the radiant source used was a strip of platinum covered with fluorine or powdered quartz1 which emits numerous radiations close to two bands of linear absorption in the absorption spectra of fluorine and quartz1 one of which is situated in the infra-red4 ,the radiations thus emitted are several times reflected on fluorine or on quartz1 as the case may be2 and as1 in proximity to the bands1 the absorption is of the order of that of metallic bodies for luminous rays1 we no longer meet in the pencil several times reflected or in the rays remaining after this kind of filtration1 with any but radiations of great wave-length4 ,thus1 for instance1 in the case of the quartz1 in the neighbourhood of a radiation corresponding to a wave-length of #h4e microns1 the absorption is thirty times greater in the region of the band than in the neighbouring region1 and consequently1 after three reflexions1 while the corresponding radiations will not have been weakened1 the neighbouring waves will be so1 on the contrary1 in the proportion of #a to #bg1jjj4 ,with mirrors of rock salt and of sylvine#ba there have been obtained1 by taking an incandescent gas light 7,auer7 as source1 radiations extending as far as #gj microns2 and these last are the greatest wave-lengths observed in optical phenomena4 ,these radiations are largely absorbed by the vapour of water1 and it is no doubt owing to this absorption that they are not found in the solar spectrum4 ,on the other hand1 they easily pass through gutta-percha1 india-rubber1 and insulating substances in general4 ,footnote #ba3 ,a natural chlorate of potassium1 generally of volcanic origin4--,,ed4 ,at the opposite end of the spectrum the knowledge of the ultra-violet regions has been greatly extended by the researches of ,lenard4 ,these extremely rapid radiations have been shown by that eminent physicist to occur in the light of the electric sparks which flash between two metal points1 and which are produced by a large induction coil with condenser and a ,wehnelt break4 ,professor ,schumann has succeeded in photographing them by depositing bromide of silver directly on glass plates without fixing it with gelatine2 and he has1 by the same process1 photographed in the spectrum of hydrogen a ray with a wave-length of only #j4a micron4 ,the spectroscope was formed entirely of fluor-spar1 and a vacuum had been created in it1 for these radiations are extremely absorbable by the air4 ,notwithstanding the extreme smallness of the luminous wave-lengths1 it has been possible1 after numerous fruitless trials1 to obtain stationary waves analogous to those which1 in the case of sound1 are produced in organ pipes4 ,the marvellous application ,m4 ,lippmann has made of these waves to completely solve the problem of photography in colours is well known4 ,this discovery1 so important in itself and so instructive1 since it shows us how the most delicate anticipations of theory may be verified in all their consequences1 and lead the physicist to the solution of the problems occurring in practice1 has justly become popular1 and there is1 therefore1 no need to describe it here in detail4 ,professor ,wiener obtained stationary waves some little while before ,m4 ,lippmann's discovery1 in a layer of a sensitive substance having a grain sufficiently small in relation to the length of wave4 ,his aim was to solve a question of great importance to a complete knowledge of the ether4 ,fresnel founded his theory of double refraction and reflexion by transparent surfaces1 on the hypothesis that the vibration of a ray of polarized light is perpendicular to the plane of polarization4 ,but ,neumann has proposed1 on the contrary1 a theory in which he recognizes that the luminous vibration is in this very plane4 ,he rather supposes1 in opposition to ,fresnel's idea1 that the density of the ether remains the same in all media1 while its coefficient of elasticity is variable4 ,very remarkable experiments on dispersion by ,m4 ,carvallo prove indeed that the idea of ,fresnel was1 if not necessary for us to adopt1 at least the more probable of the two2 but apart from this indication1 and contrary to the hypothesis of ,neumann1 the two theories1 from the point of view of the explanation of all known facts1 really appear to be equivalent4 ,are we then in presence of two mechanical explanations1 different indeed1 but nevertheless both adaptable to all the facts1 and between which it will always be impossible to make a choice8 ,or1 on the contrary1 shall we succeed in realising an experimentum crucis1 an experiment at the point where the two theories cross1 which will definitely settle the question8 ,professor ,wiener thought he could draw from his experiment a firm conclusion on the point in dispute4 ,he produced stationary waves with light polarized at an angle of #de1bb and established that1 when light is polarized in the plane of incidence1 the fringes persist2 but that1 on the other hand1 they disappear when the light is polarized perpendicularly to this plane4 ,if it be admitted that a photographic impression results from the active force of the vibratory movement of the ether1 the question is1 in fact1 completely elucidated1 and the discrepancy is abolished in ,fresnel's favour4 ,footnote #bb3 ,that is to say1 he reflected the beam of polarized light by a mirror placed at that angle4 ,see ,turpain1 ,leons lementaires de ,physique1 t4 ii4 p4 #caa1 for details of the experiment4--,,ed4 ,m4,h4 ,poincar has pointed out1 however1 that we know nothing as to the mechanism of the photographic impression4 ,we cannot consider it evident that it is the kinetic energy of the ether which produces the decomposition of the sensitive salt2 and if1 on the contrary1 we suppose it to be due to the potential energy1 all the conclusions are reversed1 and ,neumann's idea triumphs4 ,recently a very clever physicist1 ,m4 ,cotton1 especially known for his skilful researches in the domain of optics1 has taken up anew the study of stationary waves4 ,he has made very precise quantitative experiments1 and has demonstrated1 in his turn1 that it is impossible1 even with spherical waves1 to succeed in determining on which of the two vectors which have to be regarded in all theories of light on the subject of polarization phenomena the luminous intensity and the chemical action really depend4 ,this question1 therefore1 no longer exists for those physicists who admit that luminous vibrations are electrical oscillations4 ,whatever1 then1 the hypothesis formed1 whether it be electric force or1 on the contrary1 magnetic force which we place in the plane of polarization1 the mode of propagation foreseen will always be in accord with the facts observed4 #c4 ,,the ,,electromagnetic ,,ether ,the idea of attributing the phenomena of electricity to perturbations produced in the medium which transmits the light is already of old standing2 and the physicists who witnessed the triumph of ,fresnel's theories could not fail to conceive that this fluid1 which fills the whole of space and penetrates into all bodies1 might also play a preponderant part in electrical actions4 ,some even formed too hasty hypotheses on this point2 for the hour had not arrived when it was possible to place them on a sufficiently sound basis1 and the known facts were not numerous enough to give the necessary precision4 ,the founders of modern electricity also thought it wiser to adopt1 with regard to this science1 the attitude taken by ,newton in connection with gravitation3 ,in the first place to observe facts1 to vary the circumstances of these as much as possible1 to accompany this first work by precise measurements in order to deduce from them general laws founded solely on experiment1 and to deduce from these laws1 independently of all hypotheses on the nature of the forces producing the phenomena1 the mathematical value of these forces--that is to say1 the formula representing them4 ,such was the system pursued by ,newton4 ,it has1 in general1 been adopted in ,france by the scholars to whom physics owe the great progress made of late years1 and it has served as my guide in all my researches on electrodynamic phenomena4444 ,it is for this reason that ,i have avoided speaking of the ideas ,i may have on the nature of the cause of the force emanating from voltaic conductors4 ,thus did ,ampre express himself4 ,the illustrious physicist rightly considered the results obtained by him through following this wise method as worthy of comparison with the laws of attraction2 but he knew that when this first halting-place was reached there was still further to go1 and that the evolution of ideas must necessarily continue4 ,with whatever physical cause1 he adds1 we may wish to connect the phenomena produced by electro-dynamic action1 the formula ,i have obtained will always remain the expression of the facts1 and he explicitly indicated that if one could succeed in deducing his formula from the consideration of the vibrations of a fluid distributed through space1 an enormous step would have been taken in this department of physics4 ,he added1 however1 that this research appeared to him premature1 and would change nothing in the results of his work1 since1 to accord with facts1 the hypothesis adopted would always have to agree with the formula which exactly represents them4 ,it is not devoid of interest to observe that ,ampre himself1 notwithstanding his caution1 really formed some hypotheses1 and recognized that electrical phenomena were governed by the laws of mechanics4 ,yet the principles of ,newton then appeared to be unshakable4 ,faraday was the first to demonstrate1 by clear experiment1 the influence of the media in electricity and magnetic phenomena1 and he attributed this influence to certain modifications in the ether which these media enclose4 ,his fundamental conception was to reject action at a distance1 and to localize in the ether the energy whose evolution is the cause of the actions manifested1 as1 for example1 in the discharge of a condenser4 ,consider the barrel of a pump placed in a vacuum and closed by a piston at each end1 and let us introduce between these a certain mass of air4 ,the two pistons1 through the elastic force of the gas1 repel each other with a force which1 according to the law of ,mariotte1 varies in inverse ratio to the distance4 ,the method favoured by ,ampre would first of all allow this law of repulsion between the two pistons to be discovered1 even if the existence of a gas enclosed in the barrel of the pump were unsuspected2 and it would then be natural to localize the potential energy of the system on the surface of the two pistons4 ,but if the phenomenon is more carefully examined1 we shall discover the presence of the air1 and we shall understand that every part of the volume of this air could1 if it were drawn off into a recipient of equal volume1 carry away with it a fraction of the energy of the system1 and that consequently this energy belongs really to the air and not to the pistons1 which are there solely for the purpose of enabling this energy to manifest its existence4 ,faraday made1 in some sort1 an equivalent discovery when he perceived that the electrical energy belongs1 not to the coatings of the condenser1 but to the dielectric which separates them4 ,his audacious views revealed to him a new world1 but to explore this world a surer and more patient method was needed4 ,maxwell succeeded in stating with precision certain points of ,faraday's ideas1 and he gave them the mathematical form which1 often wrongly1 impresses physicists1 but which when it exactly encloses a theory1 is a certain proof that this theory is at least coherent and logical4#bc ,footnote #bc3 ,it will no doubt be a shock to those whom ,professor ,henry ,armstrong has lately called the mathematically-minded to find a member of the ,poincar family speaking disrespectfully of the science they have done so much to illustrate4 ,one may perhaps compare the expression in the text with ,m4 ,henri ,poincar's remark in his last allocution to the ,acadmie des ,sciences1 that ,mathematics are sometimes a nuisance1 and even a danger1 when they induce us to affirm more than we know 7,comptes-rendus1 #agth ,december #aijf74 ,the work of ,maxwell is over-elaborated1 complex1 difficult to read1 and often ill-understood1 even at the present day4 ,maxwell is more concerned in discovering whether it is possible to give an explanation of electrical and magnetic phenomena which shall be founded on the mechanical properties of a single medium1 than in stating this explanation in precise terms4 ,he is aware that if we could succeed in constructing such an interpretation1 it would be easy to propose an infinity of others1 entirely equivalent from the point of view of the experimentally verifiable consequences2 and his especial ambition is therefore to extract from the premises a general view1 and to place in evidence something which would remain the common property of all the theories4 ,he succeeded in showing that if the electrostatic energy of an electromagnetic field be considered to represent potential energy1 and its electrodynamic the kinetic energy1 it becomes possible to satisfy both the principle of least action and that of the conservation of energy2 from that moment--if we eliminate a few difficulties which exist regarding the stability of the solutions--the possibility of finding mechanical explanations of electromagnetic phenomena must be considered as demonstrated4 ,he thus succeeded1 moreover1 in stating precisely the notion of two electric and magnetic fields which are produced in all points of space1 and which are strictly inter-connected1 since the variation of the one immediately and compulsorily gives birth to the other4 ,from this hypothesis he deduced that1 in the medium where this energy is localized1 an electromagnetic wave is propagated with a velocity equal to the relation of the units of electric mass in the electromagnetic and electrostatic systems4 ,now1 experiments made known since his time have proved that this relation is numerically equal to the speed of light1 and the more precise experiments made in consequence--among which should be cited the particularly careful ones of ,m4 ,max ,abraham--have only rendered the coincidence still more complete4 ,it is natural henceforth to suppose that this medium is identical with the luminous ether1 and that a luminous wave is an electromagnetic wave--that is to say1 a succession of alternating currents1 which exist in the dielectric and even in the void1 and possess an enormous frequency1 inasmuch as they change their direction thousands of billions of times per second1 and by reason of this frequency produce considerable induction effects4 ,maxwell did not admit the existence of open currents4 ,to his mind1 therefore1 an electrical vibration could not produce condensations of electricity4 ,it was1 in consequence1 necessarily transverse1 and thus coincided with the vibration of ,fresnel2 while the corresponding magnetic vibration was perpendicular to it1 and would coincide with the luminous vibration of ,neumann4 ,maxwell's theory thus establishes a close correlation between the phenomena of the luminous and those of the electromagnetic waves1 or1 we might even say1 the complete identity of the two4 ,but it does not follow from this that we ought to regard the variation of an electric field produced at some one point as necessarily consisting of a real displacement of the ether round that point4 ,the idea of thus bringing electrical phenomena back to the mechanics of the ether is not1 then1 forced upon us1 and the contrary idea even seems more probable4 ,it is not the optics of ,fresnel which absorbs the science of electricity1 it is rather the optics which is swallowed up by a more general theory4 ,the attempts of popularizers who endeavour to represent1 in all their details1 the mechanism of the electric phenomena1 thus appear vain enough1 and even puerile4 ,it is useless to find out to what material body the ether may be compared1 if we content ourselves with seeing in it a medium of which1 at every point1 two vectors define the properties4 ,for a long time1 therefore1 we could remark that the theory of ,fresnel simply supposed a medium in which something periodical was propagated1 without its being necessary to admit this something to be a movement2 but we had to wait not only for ,maxwell1 but also for ,hertz1 before this idea assumed a really scientific shape4 ,hertz insisted on the fact that the six equations of the electric field permit all the phenomena to be anticipated without its being necessary to construct one hypothesis or another1 and he put these equations into a very symmetrical form1 which brings completely in evidence the perfect reciprocity between electrical and magnetic actions4 ,he did yet more1 for he brought to the ideas of ,maxwell the most striking confirmation by his memorable researches on electric oscillations4 #d4 ,,electrical ,,oscillations ,the experiments of ,hertz are well known4 ,we know how the ,bonn physicist developed1 by means of oscillating electric discharges1 displacement currents and induction effects in the whole of the space round the spark-gap2 and how he excited by induction at some point in a wire a perturbation which afterwards is propagated along the wire1 and how a resonator enabled him to detect the effect produced4 ,the most important point made evident by the observation of interference phenomena and subsequently verified directly by ,m4 ,blondlot1 is that the electromagnetic perturbation is propagated with the speed of light1 and this result condemns for ever all the hypotheses which fail to attribute any part to the intervening media in the propagation of an induction phenomenon4 ,if the inducing action were1 in fact1 to operate directly between the inducing and the induced circuits1 the propagation should be instantaneous2 for if an interval were to occur between the moment when the cause acted and the one when the effect was produced1 during this interval there would no longer be anything anywhere1 since the intervening medium does not come into play1 and the phenomenon would then disappear4 ,leaving on one side the manifold but purely electrical consequences of this and the numerous researches relating to the production or to the properties of the waves--some of which1 those of ,,mm4 ,sarrazin and de la ,rive1 ,righi1 ,turpain1 ,lebedeff1 ,decombe1 ,barbillon1 ,drude1 ,gutton1 ,lamotte1 ,lecher1 etc41 are1 however1 of the highest order--,i shall only mention here the studies more particularly directed to the establishment of the identity of the electromagnetic and the luminous waves4 ,the only differences which subsist are necessarily those due to the considerable discrepancy which exists between the durations of the periods of these two categories of waves4 ,the length of wave corresponding to the first spark-gap of ,hertz was about #f metres1 and the longest waves perceptible by the retina are #g_/aj of a micron4#bd ,footnote #bd3 ,see footnote #c4 ,these radiations are so far apart that it is not astonishing that their properties have not a perfect similitude4 ,thus phenomena like those of diffraction1 which are negligible in the ordinary conditions under which light is observed1 may here assume a preponderating importance4 ,to play the part1 for example1 with the ,hertzian waves1 which a mirror #a millimetre square plays with regard to light1 would require a colossal mirror which would attain the size of a myriametre#be square4 ,footnote #be3 ,i4e41 #aj1jjj metres4--,,ed4 ,the efforts of physicists have to-day1 however1 filled up1 in great part1 this interval1 and from both banks at once they have laboured to build a bridge between the two domains4 ,we have seen how ,rubens showed us calorific rays #fj metres long2 on the other hand1 ,,mm4 ,lecher1 ,bose1 and ,lampa have succeeded1 one after the other1 in gradually obtaining oscillations with shorter and shorter periods4 ,there have been produced1 and are now being studied1 electromagnetic waves of four millimetres2 and the gap subsisting in the spectrum between the rays left undetected by sylvine and the radiations of ,m4 ,lampa now hardly comprise more than five octaves--that is to say1 an interval perceptibly equal to that which separates the rays observed by ,m4 ,rubens from the last which are evident to the eye4 ,the analogy then becomes quite close1 and in the remaining rays the properties1 so to speak1 characteristic of the ,hertzian waves1 begin to appear4 ,for these waves1 as we have seen1 the most transparent bodies are the most perfect electrical insulators2 while bodies still slightly conducting are entirely opaque4 ,the index of refraction of these substances tends in the case of great wave-lengths to become1 as the theory anticipates1 nearly the square root of the dielectric constant4 ,,mm4 ,rubens and ,nichols have even produced with the waves which remain phenomena of electric resonance quite similar to those which an ,italian scholar1 ,m4 ,garbasso1 obtained with electric waves4 ,this physicist showed that1 if the electric waves are made to impinge on a flat wooden stand1 on which are a series of resonators parallel to each other and uniformly arranged1 these waves are hardly reflected save in the case where the resonators have the same period as the spark-gap4 ,if the remaining rays are allowed to fall on a glass plate silvered and divided by a diamond fixed on a dividing machine into small rectangles of equal dimensions1 there will be observed variations in the reflecting power according to the orientation of the rectangles1 under conditions entirely comparable with the experiment of ,garbasso4 ,in order that the phenomenon be produced it is necessary that the remaining waves should be previously polarized4 ,this is because1 in fact1 the mechanism employed to produce the electric oscillations evidently gives out vibrations which occur on a single plane and are subsequently polarized4 ,we cannot therefore entirely assimilate a radiation proceeding from a spark-gap to a ray of natural light4 ,for the synthesis of light to be realized1 still other conditions must be complied with4 ,during a luminous impression1 the direction and the phase change millions of times in the vibration sensible to the retina1 yet the damping of this vibration is very slow4 ,with the ,hertzian oscillations all these conditions are changed--the damping is very rapid but the direction remains invariable4 ,every time1 however1 that we deal with general phenomena which are independent of these special conditions1 the parallelism is perfect2 and with the waves1 we have put in evidence the reflexion1 refraction1 total reflexion1 double reflexion1 rotatory polarization1 dispersion1 and the ordinary interferences produced by rays travelling in the same direction and crossing each other at a very acute angle1 or the interferences analogous to those which ,wiener observed with rays of the contrary direction4 ,a very important consequence of the electromagnetic theory foreseen by ,maxwell is that the luminous waves which fall on a surface must exercise on this surface a pressure equal to the radiant energy which exists in the unit of volume of the surrounding space4 ,m4 ,lebedeff a few years ago allowed a sheaf of rays from an arc lamp to fall on a deflection radiometer1#bf and thus succeeded in revealing the existence of this pressure4 ,its value is sufficient1 in the case of matter of little density and finely divided1 to reduce and even change into repulsion the attractive action exercised on bodies by the sun4 ,this is a fact formerly conjectured by ,faye1 and must certainly play a great part in the deformation of the heads of comets4 ,footnote #bf3 ,by this ,m4 ,poincar appears to mean a radiometer in which the vanes are not entirely free to move as in the radiometer of ,crookes but are suspended by one or two threads as in the instrument devised by ,professor ,poynting4--,,ed4 ,more recently1 ,,mm4 ,nichols and ,hull have undertaken experiments on this point4 ,they have measured not only the pressure1 but also the energy of the radiation by means of a special bolometer4 ,they have thus arrived at numerical verifications which are entirely in conformity with the calculations of ,maxwell4 ,the existence of these pressures may be otherwise foreseen even apart from the electromagnetic theory1 by adding to the theory of undulations the principles of thermodynamics4 ,bartoli1 and more recently ,dr ,larmor1 have shown1 in fact1 that if these pressures did not exist1 it would be possible1 without any other phenomenon1 to pass heat from a cold into a warm body1 and thus transgress the principle of ,carnot4 #e4 ,,the ,x ,,rays ,it appears to-day quite probable that the ,x rays should be classed among the phenomena which have their seat in the luminous ether4 ,doubtless it is not necessary to recall here how1 in ,december #ahie1 ,rntgen1 having wrapped in black paper a ,crookes tube in action1 observed that a fluorescent platinocyanide of barium screen placed in the neighbourhood1 had become visible in the dark1 and that a photographic plate had received an impress4 ,the rays which come from the tube1 in conditions now well known1 are not deviated by a magnet1 and1 as ,m4 ,curie and ,m4 ,sagnac have conclusively shown1 they carry no electric charge4 ,they are subject to neither reflection nor refraction1 and very precise and very ingenious measurements by ,m4 ,gouy have shown that1 in their case1 the refraction index of the various bodies cannot be more than a millionth removed from unity4 ,we knew from the outset that there existed various ,x rays differing from each other as1 for instance1 the colours of the spectrum1 and these are distinguished from each other by their unequal power of passing through substances4 ,m4 ,sagnac1 particularly1 has shown that there can be obtained a gradually decreasing scale of more or less absorbable rays1 so that the greater part of their photographic action is stopped by a simple sheet of black paper4 ,these rays figure among the secondary rays discovered1 as is known1 by this ingenious physicist4 ,the ,x rays falling on matter are thus subjected to transformations which may be compared to those which the phenomena of luminescence produce on the ultra-violet rays4 ,m4 ,benoist has founded on the transparency of matter to the rays a sure and practical method of allowing them to be distinguished1 and has thus been enabled to define a specific character analogous to the colour of the rays of light4 ,it is probable also that the different rays do not transport individually the same quantity of energy4 ,we have not yet obtained on this point precise results1 but it is roughly known1 since the experiments of ,,mm4 ,rutherford and ,m',clung1 what quantity of energy corresponds to a pencil of ,x rays4 ,these physicists have found that this quantity would be1 on an average1 five hundred times larger than that brought by an analogous pencil of solar light to the surface of the earth4 ,what is the nature of this energy8 ,the question does not appear to have been yet solved4 ,it certainly appears1 according to ,professors ,haga and ,wind and to ,professor ,sommerfeld1 that with the ,x rays curious experiments of diffraction may be produced4 ,dr ,barkla has shown also that they can manifest true polarization4 ,the secondary rays emitted by a metallic surface when struck by ,x rays vary1 in fact1 in intensity when the position of the plane of incidence round the primary pencil is changed4 ,various physicists have endeavoured to measure the speed of propagation1 but it seems more and more probable that it is very nearly that of light4#bg ,footnote #bg3 ,see especially the experiments of ,professor ,e4 ,marx 7,vienna71 ,annalen der ,physik1 vol4 xx4 7,no4 #i of #aijf71 pp4 #fgg et seq41 which seem conclusive on this point4--,,ed4 ,i must here leave out the description of a crowd of other experiments4 ,some very interesting researches by ,m4 ,brunhes1 ,m4 ,broca1 ,m4 ,colardeau1 ,m4 ,villard1 in ,france1 and by many others abroad1 have permitted the elucidation of several interesting problems relative to the duration of the emission or to the best disposition to be adopted for the production of the rays4 ,the only point which will detain us is the important question as to the nature of the ,x rays themselves2 the properties which have just been brought to mind are those which appear essential and which every theory must reckon with4 ,the most natural hypothesis would be to consider the rays as ultra-violet radiations of very short wave-length1 or radiations which are in a manner ultra-ultra-violet4 ,this interpretation can still1 at this present moment1 be maintained1 and the researches of ,,mm4 ,buisson1 ,righi1 ,lenard1 and ,merrit ,stewart have even established that rays of very short wave-lengths produce on metallic conductors1 from the point of view of electrical phenomena1 effects quite analogous to those of the ,x rays4 ,another resemblance results also from the experiments by which ,m4 ,perreau established that these rays act on the electric resistance of selenium4 ,new and valuable arguments have thus added force to those who incline towards a theory which has the merit of bringing a new phenomenon within the pale of phenomena previously known4 ,nevertheless the shortest ultra-violet radiations1 such as those of ,m4 ,schumann1 are still capable of refraction by quartz1 and this difference constitutes1 in the minds of many physicists1 a serious enough reason to decide them to reject the more simple hypothesis4 ,moreover1 the rays of ,schumann are1 as we have seen1 extraordinarily absorbable1--so much so that they have to be observed in a vacuum4 ,the most striking property of the ,x rays is1 on the contrary1 the facility with which they pass through obstacles1 and it is impossible not to attach considerable importance to such a difference4 ,some attribute this marvellous radiation to longitudinal vibrations1 which1 as ,m4 ,duhem has shown1 would be propagated in dielectric media with a speed equal to that of light4 ,but the most generally accepted idea is the one formulated from the first by ,sir ,george ,stokes and followed up by ,professor ,wiechert4 ,according to this theory the ,x rays should be due to a succession of independent pulsations of the ether1 starting from the points where the molecules projected by the cathode of the ,crookes tube meet the anticathode4 ,these pulsations are not continuous vibrations like the radiations of the spectrum2 they are isolated and extremely short2 they are1 besides1 transverse1 like the undulations of light1 and the theory shows that they must be propagated with the speed of light4 ,they should present neither refraction nor reflection1 but1 under certain conditions1 they may be subject to the phenomena of diffraction4 ,all these characteristics are found in the ,rntgen rays4 ,professor ,j4,j4 ,thomson adopts an analogous idea1 and states the precise way in which the pulsations may be produced at the moment when the electrified particles forming the cathode rays suddenly strike the anticathode wall4 ,the electromagnetic induction behaves in such a way that the magnetic field is not annihilated when the particle stops1 and the new field produced1 which is no longer in equilibrium1 is propagated in the dielectric like an electric pulsation4 ,the electric and magnetic pulsations excited by this mechanism may give birth to effects similar to those of light4 ,their slight amplitude1 however1 is the cause of there here being neither refraction nor diffraction phenomena1 save in very special conditions4 ,if the cathode particle is not stopped in zero time1 the pulsation will take a greater amplitude1 and be1 in consequence1 more easily absorbable2 to this is probably to be attributed the differences which may exist between different tubes and different rays4 ,it is right to add that some authors1 notwithstanding the proved impossibility of deviating them in a magnetic field1 have not renounced the idea of comparing them with the cathode rays4 ,they suppose1 for instance1 that the rays are formed by electrons animated with so great a velocity that their inertia1 conformably with theories which ,i shall examine later1 no longer permit them to be stopped in their course2 this is1 for instance1 the theory upheld by ,mr ,sutherland4 ,we know1 too1 that to ,m4 ,gustave ,le ,bon they represent the extreme limit of material things1 one of the last stages before the vanishing of matter on its return to the ether4 ,everyone has heard of the ,n rays1 whose name recalls the town of ,nancy1 where they were discovered4 ,in some of their singular properties they are akin to the ,x rays1 while in others they are widely divergent from them4 ,m4 ,blondlot1 one of the masters of contemporary physics1 deeply respected by all who know him1 admired by everyone for the penetration of his mind1 and the author of works remarkable for the originality and sureness of his method1 discovered them in radiations emitted from various sources1 such as the sun1 an incandescent light1 a ,nernst lamp1 and even bodies previously exposed to the sun's rays4 ,the essential property which allows them to be revealed is their action on a small induction spark1 of which they increase the brilliancy2 this phenomenon is visible to the eye and is rendered objective by photography4 ,various other physicists and numbers of physiologists1 following the path opened by ,m4 ,blondlot1 published during #aijc and #aijd manifold but often rather hasty memoirs1 in which they related the results of their researches1 which do not appear to have been always conducted with the accuracy desirable4 ,these results were most strange2 they seemed destined to revolutionise whole regions not only of the domain of physics1 but likewise of the biological sciences4 ,unfortunately the method of observation was always founded on the variations in visibility of the spark or of a phosphorescent substance1 and it soon became manifest that these variations were not perceptible to all eyes4 ,no foreign experimenter has succeeded in repeating the experiments1 while in ,france many physicists have failed2 and hence the question has much agitated public opinion4 ,are we face to face with a very singular case of suggestion1 or is special training and particular dispositions required to make the phenomenon apparent8 ,it is not possible1 at the present moment1 to declare the problem solved2 but very recent experiments by ,m4 ,gutton and a note by ,m4 ,mascart have reanimated the confidence of those who hoped that such a scholar as ,m4 ,blondlot could not have been deluded by appearances4 ,however1 these last proofs in favour of the existence of the rays have themselves been contested1 and have not succeeded in bringing conviction to everyone4 ,it seems very probable indeed that certain of the most singular conclusions arrived at by certain authors on the subject will lapse into deserved oblivion4 ,but negative experiments prove nothing in a case like this1 and the fact that most experimenters have failed where ,m4 ,blondlot and his pupils have succeeded may constitute a presumption1 but cannot be regarded as a demonstrative argument4 ,hence we must still wait2 it is exceedingly possible that the illustrious physicist of ,nancy may succeed in discovering objective actions of the ,n rays which shall be indisputable1 and may thus establish on a firm basis a discovery worthy of those others which have made his name so justly celebrated4 ,according to ,m4 ,blondlot the ,n rays can be polarised1 refracted1 and dispersed1 while they have wavelengths comprised within 4#jjcj micron1 and 4#jgfj micron--that is to say1 between an eighth and a fifth of that found for the extreme ultra-violet rays4 ,they might be1 perhaps1 simply rays of a very short period4 ,their existence1 stripped of the parasitical and somewhat singular properties sought to be attributed to them1 would thus appear natural enough4 ,it would1 moreover1 be extremely important1 and lead1 no doubt1 to most curious applications2 it can be conceived1 in fact1 that such rays might serve to reveal what occurs in those portions of matter whose too minute dimensions escape microscopic examination on account of the phenomena of diffraction4 ,from whatever point of view we look at it1 and whatever may be the fate of the discovery1 the history of the ,n rays is particularly instructive1 and must give food for reflection to those interested in questions of scientific methods4 #f4 ,,the ,,ether ,,and ,,gravitation ,the striking success of the hypothesis of the ether in optics has1 in our own days1 strengthened the hope of being able to explain1 by an analogous representation1 the action of gravitation4 ,for a long time1 philosophers who rejected the idea that ponderability is a primary and essential quality of all bodies have sought to reduce their weight to pressures exercised in a very subtle fluid4 ,this was the conception of ,descartes1 and was perhaps the true idea of ,newton himself4 ,newton points out1 in many passages1 that the laws he had discovered were independent of the hypotheses that could be formed on the way in which universal attraction was produced1 but that with sufficient experiments the true cause of this attraction might one day be reached4 ,in the preface to the second edition of the ,optics he writes3 ,to prove that ,i have not considered weight as a universal property of bodies1 ,i have added a question as to its cause1 preferring this form of question because my interpretation does not entirely satisfy me in the absence of experiment2 and he puts the question in this shape3 ,is not this medium 7the ether7 more rarefied in the interior of dense bodies like the sun1 the planets1 the comets1 than in the empty spaces which separate them8 ,passing from these bodies to great distances1 does it not become continually denser1 and in that way does it not produce the weight of these great bodies with regard to each other and of their parts with regard to these bodies1 each body tending to leave the most dense for the most rarefied parts8 ,evidently this view is incomplete1 but we may endeavour to state it precisely4 ,if we admit that this medium1 the properties of which would explain the attraction1 is the same as the luminous ether1 we may first ask ourselves whether the action of gravitation is itself also due to oscillations4 ,some authors have endeavoured to found a theory on this hypothesis1 but we are immediately brought face to face with very serious difficulties4 ,gravity appears1 in fact1 to present quite exceptional characteristics4 ,no agent1 not even those which depend upon the ether1 such as light and electricity1 has any influence on its action or its direction4 ,all bodies are1 so to speak1 absolutely transparent to universal attraction1 and no experiment has succeeded in demonstrating that its propagation is not instantaneous4 ,from various astronomical observations1 ,laplace concluded that its velocity1 in any case1 must exceed fifty million times that of light4 ,it is subject neither to reflection nor to refraction2 it is independent of the structure of bodies2 and not only is it inexhaustible1 but also 7as is pointed out1 according to ,m4 ,hannequin1 by an ,english scholar1 ,james ,croll7 the distribution of the effects of the attracting force of a mass over the manifold particles which may successively enter the field of its action in no way diminishes the attraction it exercises on each of them respectively1 a thing which is seen nowhere else in nature4 ,nevertheless it is possible1 by means of certain hypotheses1 to construct interpretations whereby the appropriate movements of an elastic medium should explain the facts clearly enough4 ,but these movements are very complex1 and it seems almost inconceivable that the same medium could possess simultaneously the state of movement corresponding to the transmission of a luminous phenomenon and that constantly imposed on it by the transmission of gravitation4 ,another celebrated hypothesis was devised by ,lesage1 of ,geneva4 ,lesage supposed space to be overrun in all directions by currents of ultramundane corpuscles4 ,this hypothesis1 contested by ,maxwell1 is interesting4 ,it might perhaps be taken up again in our days1 and it is not impossible that the assimilation of these corpuscles to electrons might give a satisfactory image4#bh ,footnote #bh3 ,m4 ,sagnac 7,le ,radium1 ,jan4 #aijf1 p4 #ad71 following perhaps ,professors ,elster and ,geitel1 has lately taken up this idea anew4--,,ed4 ,m4 ,crmieux has recently undertaken experiments directed1 as he thinks1 to showing that the divergences between the phenomena of gravitation and all the other phenomena in nature are more apparent than real4 ,thus the evolution in the heart of the ether of a quantity of gravific energy would not be entirely isolated1 and as in the case of all evolutions of all energy of whatever kind1 it should provoke a partial transformation into energy of a different form4 ,thus again the liberated energy of gravitation would vary when passing from one material to another1 as from gases into liquids1 or from one liquid to a different one4 ,on this last point the researches of ,m4 ,crmieux have given affirmative results3 if we immerse in a large mass of some liquid several drops of another not miscible with the first1 but of identical density1 we form a mass representing no doubt a discontinuity in the ether1 and we may ask ourselves whether1 in conformity with what happens in all other phenomena of nature1 this discontinuity has not a tendency to disappear4 ,if we abide by the ordinary consequences of the ,newtonian theory of potential1 the drops should remain motionless1 the hydrostatic impulsion forming an exact equilibrium to their mutual attraction4 ,now ,m4 ,crmieux remarks that1 as a matter of fact1 they slowly approach each other4 ,such experiments are very delicate2 and with all the precautions taken by the author1 it cannot yet be asserted that he has removed all possibility of the action of the phenomena of capillarity nor all possible errors proceeding from extremely slight differences of temperature4 ,but the attempt is interesting and deserves to be followed up4 ,thus1 the hypothesis of the ether does not yet explain all the phenomena which the considerations relating to matter are of themselves powerless to interpret4 ,if we wished to represent to ourselves1 by the mechanical properties of a medium filling the whole of the universe1 all luminous1 electric1 and gravitation phenomena1 we should be led to attribute to this medium very strange and almost contradictory characteristics2 and yet it would be still more inconceivable that this medium should be double or treble1 that there should be two or three ethers each occupying space as if it were alone1 and interpenetrating it without exercising any action on one another4 ,we are thus brought1 by a close examination of facts1 rather to the idea that the properties of the ether are not wholly reducible to the rules of ordinary mechanics4 ,the physicist has therefore not yet succeeded in answering the question often put to him by the philosopher3 ,has the ether really an objective existence8 ,however1 it is not necessary to know the answer in order to utilize the ether4 ,in its ideal properties we find the means of determining the form of equations which are valid1 and to the learned detached from all metaphysical prepossession this is the essential point4 ,,chapter ,,vii ,a ,,chapter ,,in ,,the ,,history ,,of ,,science3 ,,wireless ,,telegraphy #a ,i have endeavoured in this book to set forth impartially the ideas dominant at this moment in the domain of physics1 and to make known the facts essential to them4 ,i have had to quote the authors of the principal discoveries in order to be able to class and1 in some sort1 to name these discoveries2 but ,i in no way claim to write even a summary history of the physics of the day4 ,i am not unaware that1 as has often been said1 contemporary history is the most difficult of all histories to write4 ,a certain step backwards seems necessary in order to enable us to appreciate correctly the relative importance of events1 and details conceal the full view from eyes which are too close to them1 as the trees prevent us from seeing the forest4 ,the event which produces a great sensation has often only insignificant consequences2 while another1 which seemed at the outset of the least importance and little worthy of note1 has in the long run a widespread and deep influence4 ,if1 however1 we deal with the history of a positive discovery1 contemporaries who possess immediate information1 and are in a position to collect authentic evidence at first hand1 will make1 by bringing to it their sincere testimony1 a work of erudition which may be very useful1 but which we may be tempted to look upon as very easy of execution4 ,yet such a labour1 even when limited to the study of a very minute question or of a recent invention1 is far from being accomplished without the historian stumbling over serious obstacles4 ,an invention is never1 in reality1 to be attributed to a single author4 ,it is the result of the work of many collaborators who sometimes have no acquaintance with one another1 and is often the fruit of obscure labours4 ,public opinion1 however1 wilfully simple in face of a sensational discovery1 insists that the historian should also act as judge2 and it is the historian's task to disentangle the truth in the midst of the contest1 and to declare infallibly to whom the acknowledgments of mankind should be paid4 ,he must1 in his capacity as skilled expert1 expose piracies1 detect the most carefully hidden plagiarisms1 and discuss the delicate question of priority2 while he must not be deluded by those who do not fear to announce1 in bold accents1 that they have solved problems of which they find the solution imminent1 and who1 the day after its final elucidation by third parties1 proclaim themselves its true discoverers4 ,he must rise above a partiality which deems itself excusable because it proceeds from national pride2 and1 finally1 he must seek with patience for what has gone before4 ,while thus retreating step by step he runs the risk of losing himself in the night of time4 ,an example of yesterday seems to show the difficulties of such a task4 ,among recent discoveries the invention of wireless telegraphy is one of those which have rapidly become popular1 and looks1 as it were1 an exact subject clearly marked out4 ,many attempts have already been made to write its history4 ,mr ,j4,j4 ,fahie published in ,england as early as #ahii an interesting work entitled the ,history of ,wireless ,telegraphy2 and about the same time ,m4 ,broca published in ,france a very exhaustive work named ,la ,telegraphie sans fil4 ,among the reports presented to the ,congrs international de physique 7,paris1 #aijj71 ,signor ,righi1 an illustrious ,italian scholar1 whose personal efforts have largely contributed to the invention of the present system of telegraphy1 devoted a chapter1 short1 but sufficiently complete1 of his masterly report on ,hertzian waves1 to the history of wireless telegraphy4 ,the same author1 in association with ,herr ,bernhard ,dessau1 has likewise written a more important work1 ,die ,telegraphie ohne ,draht2 and ,la ,telegraphie sans fil et les ondes lectriques of ,,mm4 ,j4 ,boulanger and ,g4 ,ferri may also be consulted with advantage1 as may ,la ,telegraphie sans fil of ,signor ,dominico ,mazotto4 ,quite recently ,mr ,a4 ,story has given us in a little volume called ,the ,story of ,wireless ,telegraphy1 a condensed but very precise recapitulation of all the attempts which have been made to establish telegraphic communication without the intermediary of a conducting wire4 ,mr ,story has examined many documents1 has sometimes brought curious facts to light1 and has studied even the most recently adopted apparatus4 ,it may be interesting1 by utilising the information supplied by these authors and supplementing them when necessary by others1 to trace the sources of this modern discovery1 to follow its developments1 and thus to prove once more how much a matter1 most simple in appearance1 demands extensive and complex researches on the part of an author desirous of writing a definitive work4 #b ,the first1 and not the least difficulty1 is to clearly define the subject4 ,the words wireless telegraphy1 which at first seem to correspond to a simple and perfectly clear idea1 may in reality apply to two series of questions1 very different in the mind of a physicist1 between which it is important to distinguish4 ,the transmission of signals demands three organs which all appear indispensable3 the transmitter1 the receiver1 and1 between the two1 an intermediary establishing the communication4 ,this intermediary is generally the most costly part of the installation and the most difficult to set up1 while it is here that the sensible losses of energy at the expense of good output occur4 ,and yet our present ideas cause us to consider this intermediary as more than ever impossible to suppress2 since1 if we are definitely quit of the conception of action at a distance1 it becomes inconceivable to us that energy can be communicated from one point to another without being carried by some intervening medium4 ,but1 practically1 the line will be suppressed if1 instead of constructing it artificially1 we use to replace it one of the natural media which separate two points on the earth4 ,these natural media are divided into two very distinct categories1 and from this classification arise two series of questions to be examined4 ,between the two points in question there are1 first1 the material media such as the air1 the earth1 and the water4 ,for a long time we have used for transmissions to a distance the elastic properties of the air1 and more recently the electric conductivity of the soil and of water1 particularly that of the sea4 ,modern physics leads us on the other hand1 as we have seen1 to consider that there exists throughout the whole of the universe another and more subtle medium which penetrates everywhere1 is endowed with elasticity in vacuo1 and retains its elasticity when it penetrates into a great number of bodies1 such as the air4 ,this medium is the luminous ether which possesses1 as we cannot doubt1 the property of being able to transmit energy1 since it itself brings to us by far the larger part of the energy which we possess on earth and which we find in the movements of the atmosphere1 or of waterfalls1 and in the coal mines proceeding from the decomposition of carbon compounds under the influence of the solar energy4 ,for a long time also before the existence of the ether was known1 the duty of transmitting signals was entrusted to it4 ,thus through the ages a double evolution is unfolded which has to be followed by the historian who is ambitious of completeness4 #c ,if such an historian were to examine from the beginning the first order of questions1 he might1 no doubt1 speak only briefly of the attempts earlier than electric telegraphy4 ,without seeking to be paradoxical1 he certainly ought to mention the invention of the speaking-trumpet and other similar inventions which for a long time have enabled mankind1 by the ingenious use of the elastic properties of the natural media1 to communicate at greater distances than they could have attained without the aid of art4 ,after this in some sort prehistoric period had been rapidly run through1 he would have to follow very closely the development of electric telegraphy4 ,almost from the outset1 and shortly after ,ampre had made public the idea of constructing a telegraph1 and the day after ,gauss and ,weber set up between their houses in ,gttingen the first line really used1 it was thought that the conducting properties of the earth and water might be made of service4 ,the history of these trials is very long1 and is closely mixed up with the history of ordinary telegraphy2 long chapters for some time past have been devoted to it in telegraphic treatises4 ,it was in #ahch1 however1 that ,professor ,c4,a4 ,steinheil of ,munich expressed1 for the first time1 the clear idea of suppressing the return wire and replacing it by a connection of the line wire to the earth4 ,he thus at one step covered half the way1 the easiest1 it is true1 which was to lead to the final goal1 since he saved the use of one-half of the line of wire4 ,steinheil1 advised1 perhaps1 by ,gauss1 had1 moreover1 a very exact conception of the part taken by the earth considered as a conducting body4 ,he seems to have well understood that1 in certain conditions1 the resistance of such a conductor1 though supposed to be unlimited1 might be independent of the distance apart of the electrodes which carry the current and allow it to go forth4 ,he likewise thought of using the railway lines to transmit telegraphic signals4 ,several scholars who from the first had turned their minds to telegraphy1 had analogous ideas4 ,it was thus that ,s4,f4,b4 ,morse1 superintendent of the ,government telegraphs in the ,united ,states1 whose name is universally known in connection with the very simple apparatus invented by him1 made experiments in the autumn of #ahdb before a special commission in ,new ,york and a numerous public audience1 to show how surely and how easily his apparatus worked4 ,in the very midst of his experiments a very happy idea occurred to him of replacing by the water of a canal1 the length of about a mile of wire which had been suddenly and accidentally destroyed4 ,this accident1 which for a moment compromised the legitimate success the celebrated engineer expected1 thus suggested to him a fruitful idea which he did not forget4 ,he subsequently repeated attempts to thus utilise the earth and water1 and obtained some very remarkable results4 ,it is not possible to quote here all the researches undertaken with the same purpose1 to which are more particularly attached the names of ,s4,w4 ,wilkins1 ,wheatstone1 and ,h4 ,highton1 in ,england2 of ,bonetti in ,italy1 ,gintl in ,austria1 ,bouchot and ,donat in ,france2 but there are some which cannot be recalled without emotion4 ,on the #agth ,december #ahgj1 a physicist who has left in the ,university of ,paris a lasting name1 ,m4 d',almeida1 at that time ,professor at the ,lyce ,henri ,,iv4 and later ,inspector-,general of ,public ,instruction1 quitted ,paris1 then besieged1 in a balloon1 and descended in the midst of the ,german lines4 ,he succeeded1 after a perilous journey1 in gaining ,havre by way of ,bordeaux and ,lyons2 and after procuring the necessary apparatus in ,england1 he descended the ,seine as far as ,poissy1 which he reached on the #adth ,january #ahga4 ,after his departure1 two other scholars1 ,,mm4 ,desains and ,bourbouze1 relieving each other day and night1 waited at ,paris1 in a wherry on the ,seine1 ready to receive the signal which they awaited with patriotic anxiety4 ,it was a question of working a process devised by the last-named pair1 in which the water of the river acted the part of the line wire4 ,on the #bcrd ,january the communication at last seemed to be established1 but unfortunately1 first the armistice and then the surrender of ,paris rendered useless the valuable result of this noble effort4 ,special mention is also due to the experiments made by the ,indian ,telegraph ,office1 under the direction of ,mr ,johnson and afterwards of ,mr ,w4,f4 ,melhuish4 ,they led1 indeed1 in #ahhi to such satisfactory results that a telegraph service1 in which the line wire was replaced by the earth1 worked practically and regularly4 ,other attempts were also made during the latter half of the nineteenth century to transmit signals through the sea4 ,they preceded the epoch when1 thanks to numerous physicists1 among whom ,lord ,kelvin undoubtedly occupies a preponderating position1 we succeeded in sinking the first cable2 but they were not abandoned1 even after that date1 for they gave hopes of a much more economical solution of the problem4 ,among the most interesting are remembered those that ,s4,w4 ,wilkins carried on for a long time between ,france and ,england4 ,like ,cooke and ,wheatstone1 he thought of using as a receiver an apparatus which in some features resembles the present receiver of the submarine telegraph4 ,later1 ,george ,e4 ,dering1 then ,james ,bowman and ,lindsay1 made on the same lines trials which are worthy of being remembered4 ,but it is only in our own days that ,sir ,william ,h4 ,preece at last obtained for the first time really practical results4 ,sir ,william himself effected and caused to be executed by his associates--he is chief consulting engineer to the ,general ,post ,office in ,england-- researches conducted with much method and based on precise theoretical considerations4 ,he thus succeeded in establishing very easy1 clear1 and regular communications between various places2 for example1 across the ,bristol ,channel4 ,the long series of operations accomplished by so many seekers1 with the object of substituting a material and natural medium for the artificial lines of metal1 thus met with an undoubted success which was soon to be eclipsed by the widely-known experiments directed into a different line by ,marconi4 ,it is right to add that ,sir ,william ,preece had himself utilised induction phenomena in his experiments1 and had begun researches with the aid of electric waves4 ,much is due to him for the welcome he gave to ,marconi2 it is certainly thanks to the advice and the material support he found in ,sir ,william that the young scholar succeeded in effecting his sensational experiments4 #d ,the starting-point of the experiments based on the properties of the luminous ether1 and having for their object the transmission of signals1 is very remote2 and it would be a very laborious task to hunt up all the work accomplished in that direction1 even if we were to confine ourselves to those in which electrical reactions play a part4 ,an electric reaction1 an electrostatic influence1 or an electromagnetic phenomenon1 is transmitted at a distance through the air by the intermediary of the luminous ether4 ,but electric influence can hardly be used1 as the distances it would allow us to traverse would be much too restricted1 and electrostatic actions are often very erratic4 ,the phenomena of induction1 which are very regular and insensible to the variations of the atmosphere1 have1 on the other hand1 for a long time appeared serviceable for telegraphic purposes4 ,we might find1 in a certain number of the attempts just mentioned1 a partial employment of these phenomena4 ,lindsay1 for instance1 in his project of communication across the sea1 attributed to them a considerable rle4 ,these phenomena even permitted a true telegraphy without intermediary wire between the transmitter and the receiver1 at very restricted distances1 it is true1 but in peculiarly interesting conditions4 ,it is1 in fact1 owing to them that ,c4 ,brown1 and later ,edison and ,gilliland1 succeeded in establishing communications with trains in motion4 ,mr ,willoughby ,s4 ,smith and ,mr ,charles ,a4 ,stevenson also undertook experiments during the last twenty years1 in which they used induction1 but the most remarkable attempts are perhaps those of ,professor ,emile ,rathenau4 ,with the assistance of ,professor ,rubens and of ,herr ,w4 ,rathenau1 this physicist effected1 at the request of the ,german ,ministry of ,marine1 a series of researches which enabled him1 by means of a compound system of conduction and induction by alternating currents1 to obtain clear and regular communications at a distance of four kilometres4 ,among the precursors also should be mentioned ,graham ,bell2 the inventor of the telephone thought of employing his admirable apparatus as a receiver of induction phenomena transmitted from a distance2 ,edison1 ,herr ,sacher of ,vienna1 ,m4 ,henry ,dufour of ,lausanne1 and ,professor ,trowbridge of ,boston1 also made interesting attempts in the same direction4 ,in all these experiments occurs the idea of employing an oscillating current4 ,moreover1 it was known for a long time--since1 in #ahdb1 the great ,american physicist ,henry proved that the discharges from a ,leyden jar in the attic of his house caused sparks in a metallic circuit on the ground floor--that a flux which varies rapidly and periodically is much more efficacious than a simple flux1 which latter can only produce at a distance a phenomenon of slight intensity4 ,this idea of the oscillating current was closely akin to that which was at last to lead to an entirely satisfactory solution3 that is1 to a solution which is founded on the properties of electric waves4 #e ,having thus got to the threshold of the definitive edifice1 the historian1 who has conducted his readers over the two parallel routes which have just been marked out1 will be brought to ask himself whether he has been a sufficiently faithful guide and has not omitted to draw attention to all essential points in the regions passed through4 ,ought we not to place by the side1 or perhaps in front1 of the authors who have devised the practical appliances1 those scholars who have constructed the theories and realised the laboratory experiments of which1 after all1 the apparatus are only the immediate applications8 ,if we speak of the propagation of a current in a material medium1 can one forget the names of ,fourier and of ,ohm1 who established by theoretical considerations the laws which preside over this propagation8 ,when one looks at the phenomena of induction1 would it not be just to remember that ,arago foresaw them1 and that ,michael ,faraday discovered them8 ,it would be a delicate1 and also a rather puerile task1 to class men of genius in order of merit4 ,the merit of an inventor like ,edison and that of a theorist like ,clerk ,maxwell have no common measure1 and mankind is indebted for its great progress to the one as much as to the other4 ,before relating how success attended the efforts to utilise electric waves for the transmission of signals1 we cannot without ingratitude pass over in silence the theoretical speculations and the work of pure science which led to the knowledge of these waves4 ,it would therefore be just1 without going further back than ,faraday1 to say how that illustrious physicist drew attention to the part taken by insulating media in electrical phenomena1 and to insist also on the admirable memoirs in which for the first time ,clerk ,maxwell made a solid bridge between those two great chapters of ,physics1 optics and electricity1 which till then had been independent of each other4 ,and no doubt it would be impossible not to evoke the memory of those who1 by establishing1 on the other hand1 the solid and magnificent structure of physical optics1 and proving by their immortal works the undulatory nature of light1 prepared from the opposite direction the future unity4 ,in the history of the applications of electrical undulations1 the names of ,young1 ,fresnel1 ,fizeau1 and ,foucault must be inscribed2 without these scholars1 the assimilation between electrical and luminous phenomena which they discovered and studied would evidently have been impossible4 ,since there is an absolute identity of nature between the electric and the luminous waves1 we should1 in all justice1 also consider as precursors those who devised the first luminous telegraphs4 ,claude ,chappe incontestably effected wireless telegraphy1 thanks to the luminous ether1 and the learned men1 such as ,colonel ,mangin1 who perfected optical telegraphy1 indirectly suggested certain improvements lately introduced into the present method4 ,but the physicist whose work should most of all be put in evidence is1 without fear of contradiction1 ,heinrich ,hertz4 ,it was he who demonstrated irrefutably1 by experiments now classic1 that an electric discharge produces an undulatory disturbance in the ether contained in the insulating media in its neighbourhood2 it was he who1 as a profound theorist1 a clever mathematician1 and an experimenter of prodigious dexterity1 made known the mechanism of the production1 and fully elucidated that of the propagation of these electromagnetic waves4 ,he must naturally himself have thought that his discoveries might be applied to the transmission of signals4 ,it would appear1 however1 that when interrogated by a ,munich engineer named ,huber as to the possibility of utilising the waves for transmissions by telephone1 he answered in the negative1 and dwelt on certain considerations relative to the difference between the periods of sounds and those of electrical vibrations4 ,this answer does not allow us to judge what might have happened1 had not a cruel death carried off in #ahid1 at the age of thirty-five1 the great and unfortunate physicist4 ,we might also find in certain works earlier than the experiments of ,hertz attempts at transmission in which1 unconsciously no doubt1 phenomena were already set in operation which would1 at this day1 be classed as electric oscillations4 ,it is allowable no doubt1 not to speak of an ,american quack1 ,mahlon ,loomis1 who1 according to ,mr ,story1 patented in #ahgj a project of communication in which he utilised the ,rocky ,mountains on one side and ,mont ,blanc on the other1 as gigantic antennae to establish communication across the ,atlantic2 but we cannot pass over in silence the very remarkable researches of the ,american ,professor ,dolbear1 who showed1 at the electrical exhibition of ,philadelphia in #ahhd1 a set of apparatus enabling signals to be transmitted at a distance1 which he described as an exceptional application of the principles of electrostatic induction4 ,this apparatus comprised groups of coils and condensers by means of which he obtained1 as we cannot now doubt1 effects due to true electric waves4 ,place should also be made for a well-known inventor1 ,d4,e4 ,hughes1 who from #ahgi to #ahhf followed up some very curious experiments in which also these oscillations certainly played a considerable part4 ,it was this physicist who invented the microphone1 and thus1 in another way1 drew attention to the variations of contact resistance1 a phenomenon not far from that produced in the radio-conductors of ,branly1 which are important organs in the ,marconi system4 ,unfortunately1 fatigued and in ill-health1 ,hughes ceased his researches at the moment perhaps when they would have given him final results4 ,in an order of ideas different in appearance1 but closely linked at bottom with the one just mentioned1 must be recalled the discovery of radiophony in #ahhj by ,graham ,bell1 which was foreshadowed in #ahge by ,c4,a4 ,brown4 ,a luminous ray falling on a selenium cell produces a variation of electric resistance1 thanks to which a sound signal can be transmitted by light4 ,that delicate instrument the radiophone1 constructed on this principle1 has wide analogies with the apparatus of to-day4 #f ,starting from the experiments of ,hertz1 the history of wireless telegraphy almost merges into that of the researches on electrical waves4 ,all the progress realised in the manner of producing and receiving these waves necessarily helped to give rise to the application already indicated4 ,the experiments of ,hertz1 after being checked in every laboratory1 and having entered into the strong domain of our most certain knowledge1 were about to yield the expected fruit4 ,experimenters like ,sir ,oliver ,lodge in ,england1 ,righi in ,italy1 ,sarrazin and de la ,rive in ,switzerland1 ,blondlot in ,france1 ,lecher in ,germany1 ,bose in ,india1 ,lebedeff in ,russia1 and theorists like ,m4,h4 ,poincar and ,professor ,bjerknes1 who devised ingenious arrangements or elucidated certain points left dark1 are among the artisans of the work which followed its natural evolution4 ,it was ,professor ,r4 ,threlfall who seems to have been the first to clearly propose1 in #ahij1 the application of the ,hertzian waves to telegraphy1 but it was certainly ,sir ,w4 ,crookes who1 in a very remarkable article in the ,fortnightly ,review of ,february #ahib1 pointed out very clearly the road to be followed4 ,he even showed in what conditions the ,morse receiver might be applied to the new system of telegraphy4 ,about the same period an ,american physicist1 well known by his celebrated experiments on high frequency currents--experiments1 too1 which are not unconnected with those on electric oscillations1--,m4 ,tesla1 demonstrated that these oscillations could be transmitted to more considerable distances by making use of two vertical antennae1 terminated by large conductors4 ,a little later1 ,sir ,oliver ,lodge succeeded1 by the aid of the coherer1 in detecting waves at relatively long distances1 and ,mr ,rutherford obtained similar results with a magnetic indicator of his own invention4 ,an important question of meteorology1 the study of atmospheric discharges1 at this date led a few scholars1 and more particularly the ,russian1 ,m4 ,popoff1 to set up apparatus very analogous to the receiving apparatus of the present wireless telegraphy4 ,this comprised a long antenna and filings-tube1 and ,m4 ,popoff even pointed out that his apparatus might well serve for the transmission of signals as soon as a generator of waves powerful enough had been discovered4 ,finally1 on the #bnd ,june #ahif1 a young ,italian1 born in ,bologna on the #beth ,april #ahgd1 ,guglielmo ,marconi1 patented a system of wireless telegraphy destined to become rapidly popular4 ,brought up in the laboratory of ,professor ,righi1 one of the physicists who had done most to confirm and extend the experiments of ,hertz1 ,marconi had long been familiar with the properties of electric waves1 and was well used to their manipulation4 ,he afterwards had the good fortune to meet ,sir ,william 7then ,mr7 ,preece1 who was to him an adviser of the highest authority4 ,it has sometimes been said that the ,marconi system contains nothing original2 that the apparatus for producing the waves was the oscillator of ,righi1 that the receiver was that employed for some two or three years by ,professor ,lodge and ,mr ,bose1 and was founded on an earlier discovery by a ,french scholar1 ,m4 ,branly2 and1 finally1 that the general arrangement was that established by ,m4 ,popoff4 ,the persons who thus rather summarily judge the work of ,m4 ,marconi show a severity approaching injustice4 ,it cannot1 in truth1 be denied that the young scholar has brought a strictly personal contribution to the solution of the problem he proposed to himself4 ,apart from his forerunners1 and when their attempts were almost unknown1 he had the very great merit of adroitly arranging the most favourable combination1 and he was the first to succeed in obtaining practical results1 while he showed that the electric waves could be transmitted and received at distances enormous compared to those attained before his day4 ,alluding to a well-known anecdote relating to ,christopher ,columbus1 ,sir ,w4 ,preece very justly said3 ,the forerunners and rivals of ,marconi no doubt knew of the eggs1 but he it was who taught them to make them stand on end4 ,this judgment will1 without any doubt1 be the one that history will definitely pronounce on the ,italian scholar4 #g ,the apparatus which enables the electric waves to be revealed1 the detector or indicator1 is the most delicate organ in wireless telegraphy4 ,it is not necessary to employ as an indicator a filings-tube or radio-conductor4 ,one can1 in principle1 for the purpose of constructing a receiver1 think of any one of the multiple effects produced by the ,hertzian waves4 ,in many systems in use1 and in the new one of ,marconi himself1 the use of these tubes has been abandoned and replaced by magnetic detectors4 ,nevertheless1 the first and the still most frequent successes are due to radio-conductors1 and public opinion has not erred in attributing to the inventor of this ingenious apparatus a considerable and almost preponderant part in the invention of wave telegraphy4 ,the history of the discovery of radio-conductors is short1 but it deserves1 from its importance1 a chapter to itself in the history of wireless telegraphy4 ,from a theoretical point of view1 the phenomena produced in those tubes should be set by the side of those studied by ,graham ,bell1 ,c4,a4 ,brown1 and ,summer ,tainter1 from the year #ahgh onward4 ,the variations to which luminous waves give rise in the resistance of selenium and other substances are1 doubtless1 not unconnected with those which the electric waves produce in filings4 ,a connection can also be established between this effect of the waves and the variations of contact resistance which enabled ,hughes to construct the microphone1 that admirable instrument which is one of the essential organs of telephony4 ,more directly1 as an antecedent to the discovery1 should be quoted the remark made by ,varley in #ahgj1 that coal-dust changes in conductivity when the electromotive force of the current which passes through it is made to vary4 ,but it was in #ahhd that an ,italian professor1 ,signor ,calzecchi-,onesti1 demonstrated in a series of remarkable experiments that the metallic filings contained in a tube of insulating material1 into which two metallic electrodes are inserted1 acquire a notable conductivity under different influences such as extra currents1 induced currents1 sonorous vibrations1 etc41 and that this conductivity is easily destroyed2 as1 for instance1 by turning the tube over and over4 ,in several memoirs published in #ahij and #ahia1 ,m4 ,ed4 ,branly independently pointed out similar phenomena1 and made a much more complete and systematic study of the question4 ,he was the first to note very clearly that the action described could be obtained by simply making sparks pass in the neighbourhood of the radio-conductor1 and that their great resistance could be restored to the filings by giving a slight shake to the tube or to its supports4 ,the idea of utilising such a very interesting phenomenon as an indicator in the study of the ,hertzian waves seems to have occurred simultaneously to several physicists1 among whom should be especially mentioned ,m4 ,ed4 ,branly himself1 ,sir ,oliver ,lodge1 and ,,mm4 ,le ,royer and ,van ,beschem1 and its use in laboratories rapidly became quite common4 ,the action of the waves on metallic powders has1 however1 remained some what mysterious2 for ten years it has been the subject of important researches by ,professor ,lodge1 ,m4 ,branly1 and a very great number of the most distinguished physicists4 ,it is impossible to notice here all these researches1 but from a recent and very interesting work of ,m4 ,blanc1 it would seem that the phenomenon is allied to that of ionisation4 #h ,the history of wireless telegraphy does not end with the first experiments of ,marconi2 but from the moment their success was announced in the public press1 the question left the domain of pure science to enter into that of commerce4 ,the historian's task here becomes different1 but even more delicate2 and he will encounter difficulties which can be only known to one about to write the history of a commercial invention4 ,the actual improvements effected in the system are kept secret by the rival companies1 and the most important results are patriotically left in darkness by the learned officers who operate discreetly in view of the national defence4 ,meanwhile1 men of business desirous of bringing out a company proclaim1 with great nourish of advertisements1 that they are about to exploit a process superior to all others4 ,on this slippery ground the impartial historian must nevertheless venture2 and he may not refuse to relate the progress accomplished1 which is considerable4 ,therefore1 after having described the experiments carried out for nearly ten years by ,marconi himself1 first across the ,bristol ,channel1 then at ,spezzia1 between the coast and the ironclad ,san ,bartolommeo1 and finally by means of gigantic apparatus between ,america and ,england1 he must give the names of those who1 in the different civilised countries1 have contributed to the improvement of the system of communication by waves2 while he must describe what precious services this system has already rendered to the art of war1 and happily also to peaceful navigation4 ,from the point of view of the theory of the phenomena1 very remarkable results have been obtained by various physicists1 among whom should be particularly mentioned ,m4 ,tissot1 whose brilliant studies have thrown a bright light on different interesting points1 such as the rle of the antennae4 ,it would be equally impossible to pass over in silence other recent attempts in a slightly different groove4 ,marconi's system1 however improved it may be to-day1 has one grave defect4 ,the synchronism of the two pieces of apparatus1 the transmitter and the receiver1 is not perfect1 so that a message sent off by one station may be captured by some other station4 ,the fact that the phenomena of resonance are not utilised1 further prevents the quantity of energy received by the receiver from being considerable1 and hence the effects reaped are very weak1 so that the system remains somewhat fitful and the communications are often disturbed by atmospheric phenomena4 ,causes which render the air a momentary conductor1 such as electrical discharges1 ionisation1 etc41 moreover naturally prevent the waves from passing1 the ether thus losing its elasticity4 ,professor ,ferdinand ,braun of ,strasburg has conceived the idea of employing a mixed system1 in which the earth and the water1 which1 as we have seen1 have often been utilised to conduct a current for transmitting a signal1 will serve as a sort of guide to the waves themselves4 ,the now well-known theory of the propagation of waves guided by a conductor enables it to be foreseen that1 according to their periods1 these waves will penetrate more or less deeply into the natural medium1 from which fact has been devised a method of separating them according to their frequency4 ,by applying this theory1 ,m4 ,braun has carried out1 first in the fortifications of ,strasburg1 and then between the island of ,heligoland and the mainland1 experiments which have given remarkable results4 ,we might mention also the researches1 in a somewhat analogous order of ideas1 by an ,english engineer1 ,mr ,armstrong1 by ,dr ,lee de ,forest1 and also by ,professor ,fessenden4 ,having thus arrived at the end of this long journey1 which has taken him from the first attempts down to the most recent experiments1 the historian can yet set up no other claim but that of having written the commencement of a history which others must continue in the future4 ,progress does not stop1 and it is never permissible to say that an invention has reached its final form4 ,should the historian desire to give a conclusion to his labour and answer the question the reader would doubtless not fail to put to him1 ,to whom1 in short1 should the invention of wireless telegraphy more particularly be attributed8 he should certainly first give the name of ,hertz1 the genius who discovered the waves1 then that of ,marconi1 who was the first to transmit signals by the use of ,hertzian undulations1 and should add those of the scholars who1 like ,morse1 ,popoff1 ,sir ,w4 ,preece1 ,lodge1 and1 above all1 ,branly1 have devised the arrangements necessary for their transmission4 ,but he might then recall what ,voltaire wrote in the ,philosophical ,dictionary3 ,what6 ,we wish to know what was the exact theology of ,thot1 of ,zerdust1 of ,sanchuniathon1 of the first ,brahmins1 and we are ignorant of the inventor of the shuttle6 ,the first weaver1 the first mason1 the first smith1 were no doubt great geniuses1 but they were disregarded4 ,why8 ,because none of them invented a perfected art4 ,the one who hollowed out an oak to cross a river never made a galley2 those who piled up rough stones with girders of wood did not plan the ,pyramids4 ,everything is made by degrees and the glory belongs to no one4 ,to-day1 more than ever1 the words of ,voltaire are true3 science becomes more and more impersonal1 and she teaches us that progress is nearly always due to the united efforts of a crowd of workers1 and is thus the best school of social solidarity4 ,,chapter ,,viii ,,the ,,conductivity ,,of ,,gases ,,and ,,the ,,ions #a4 ,,the ,,conductivity ,,of ,,gases ,if we were confined to the facts ,i have set forth above1 we might conclude that two classes of phenomena are to-day being interpreted with increasing correctness in spite of the few difficulties which have been pointed out4 ,the hypothesis of the molecular constitution of matter enables us to group together one of these classes1 and the hypothesis of the ether leads us to co-ordinate the other4 ,but these two classes of phenomena cannot be considered independent of each other4 ,relations evidently exist between matter and the ether1 which manifest themselves in many cases accessible to experiment1 and the search for these relations appears to be the paramount problem the physicist should set himself4 ,the question has1 for a long time1 been attacked on various sides1 but the recent discoveries in the conductivity of gases1 of the radioactive substances1 and of the cathode and similar rays1 have allowed us of late years to regard it in a new light4 ,without wishing to set out here in detail facts which for the most part are well known1 we will endeavour to group the chief of them round a few essential ideas1 and will seek to state precisely the data they afford us for the solution of this grave problem4 ,it was the study of the conductivity of gases which at the very first furnished the most important information1 and allowed us to penetrate more deeply than had till then been possible into the inmost constitution of matter1 and thus to1 as it were1 catch in the act the actions that matter can exercise on the ether1 or1 reciprocally1 those it may receive from it4 ,it might1 perhaps1 have been foreseen that such a study would prove remarkably fruitful4 ,the examination of the phenomena of electrolysis had1 in fact1 led to results of the highest importance on the constitution of liquids1 and the gaseous media which presented themselves as particularly simple in all their properties ought1 it would seem1 to have supplied from the very first a field of investigation easy to work and highly productive4 ,this1 however1 was not at all the case4 ,experimental complications springing up at every step obscured the problem4 ,one generally found one's self in the presence of violent disruptive discharges with a train of accessory phenomena1 due1 for instance1 to the use of metallic electrodes1 and made evident by the complex appearance of aigrettes and effluves2 or else one had to deal with heated gases difficult to handle1 which were confined in receptacles whose walls played a troublesome part and succeeded in veiling the simplicity of the fundamental facts4 ,notwithstanding1 therefore1 the efforts of a great number of seekers1 no general idea disengaged itself out of a mass of often contradictory information4 ,many physicists1 in ,france particularly1 discarded the study of questions which seemed so confused1 and it must even be frankly acknowledged that some among them had a really unfounded distrust of certain results which should have been considered proved1 but which had the misfortune to be in contradiction with the theories in current use4 ,all the classic ideas relating to electrical phenomena led to the consideration that there existed a perfect symmetry between the two electricities1 positive and negative4 ,in the passing of electricity through gases there is manifested1 on the contrary1 an evident dissymmetry4 ,the anode and the cathode are immediately distinguished in a tube of rarefied gas by their peculiar appearance2 and the conductivity does not appear1 under certain conditions1 to be the same for the two modes of electrification4 ,it is not devoid of interest to note that ,erman1 a ,german scholar1 once very celebrated and now generally forgotten1 drew attention as early as #ahae to the unipolar conductivity of a flame4 ,his contemporaries1 as may be gathered from the perusal of the treatises on physics of that period1 attached great importance to this discovery2 but1 as it was somewhat inconvenient and did not readily fit in with ordinary studies1 it was in due course neglected1 then considered as insufficiently established1 and finally wholly forgotten4 ,all these somewhat obscure facts1 and some others--such as the different action of ultra-violet radiations on positively and negatively charged bodies--are now1 on the contrary1 about to be co-ordinated1 thanks to the modern ideas on the mechanism of conduction2 while these ideas will also allow us to interpret the most striking dissymmetry of all1 i4e4 that revealed by electrolysis itself1 a dissymmetry which certainly can not be denied1 but to which sufficient attention has not been given4 ,it is to a ,german physicist1 ,giese1 that we owe the first notions on the mechanism of the conductivity of gases1 as we now conceive it4 ,in two memoirs published in #ahhb and #ahhi1 he plainly arrives at the conception that conduction in gases is not due to their molecules1 but to certain fragments of them or to ions4 ,giese was a forerunner1 but his ideas could not triumph so long as there were no means of observing conduction in simple circumstances4 ,but this means has now been supplied in the discovery of the ,x rays4 ,suppose we pass through some gas at ordinary pressure1 such as hydrogen1 a pencil of ,x rays4 ,the gas1 which till then has behaved as a perfect insulator1#bi suddenly acquires a remarkable conductivity4 ,if into this hydrogen two metallic electrodes in communication with the two poles of a battery are introduced1 a current is set up in very special conditions which remind us1 when they are checked by experiments1 of the mechanism which allows the passage of electricity in electrolysis1 and which is so well represented to us when we picture to ourselves this passage as due to the migration towards the electrodes1 under the action of the field1 of the two sets of ions produced by the spontaneous division of the molecule within the solution4 ,footnote #bi3 ,at least1 so long as it is not introduced between the two coatings of a condenser having a difference of potential sufficient to overcome what ,m4 ,bouty calls its dielectric cohesion4 ,we leave on one side this phenomenon1 regarding which ,m4 ,bouty has arrived at extremely important results by a very remarkable series of experiments2 but this question rightly belongs to a special study of electrical phenomena which is not yet written4 ,let us therefore recognise with ,j4,j4 ,thomson and the many physicists who1 in his wake1 have taken up and developed the idea of ,giese1 that1 under the influence of the ,x rays1 for reasons which will have to be determined later1 certain gaseous molecules have become divided into two portions1 the one positively and the other negatively electrified1 which we will call1 by analogy with the kindred phenomenon in electrolysis1 by the name of ions4 ,if the gas be then placed in an electric field1 produced1 for instance1 by two metallic plates connected with the two poles of a battery respectively1 the positive ions will travel towards the plate connected with the negative pole1 and the negative ions in the contrary direction4 ,there is thus produced a current due to the transport to the electrodes of the charges which existed on the ions4 ,if the gas thus ionised be left to itself1 in the absence of any electric field1 the ions1 yielding to their mutual attraction1 must finally meet1 combine1 and reconstitute a neutral molecule1 thus returning to their initial condition4 ,the gas in a short while loses the conductivity which it had acquired2 or this is1 at least1 the phenomenon at ordinary temperatures4 ,but if the temperature is raised1 the relative speeds of the ions at the moment of impact may be great enough to render it impossible for the recombination to be produced in its entirety1 and part of the conductivity will remain4 ,every element of volume rendered a conductor therefore furnishes1 in an electric field1 equal quantities of positive and negative electricity4 ,if we admit1 as mentioned above1 that these liberated quantities are borne by ions each bearing an equal charge1 the number of these ions will be proportional to the quantity of electricity1 and instead of speaking of a quantity of electricity1 we could use the equivalent term of number of ions4 ,for the excitement produced by a given pencil of ,x rays1 the number of ions liberated will be fixed4 ,thus1 from a given volume of gas there can only be extracted an equally determinate quantity of electricity4 ,the conductivity produced is not governed by ,ohm's law4 ,the intensity is not proportional to the electromotive force1 and it increases at first as the electromotive force augments2 but it approaches asymptotically to a maximum value which corresponds to the number of ions liberated1 and can therefore serve as a measure of the power of the excitement4 ,it is this current which is termed the current of saturation4 ,m4 ,righi has ably demonstrated that ionised gas does not obey the law of ,ohm by an experiment very paradoxical in appearance4 ,he found that1 the greater the distance of the two electrode plates from each1 the greater may be1 within certain limits1 the intensity of the current4 ,the fact is very clearly interpreted by the theory of ionisation1 since the greater the length of the gaseous column the greater must be the number of ions liberated4 ,one of the most striking characteristics of ionised gases is that of discharging electrified conductors4 ,this phenomenon is not produced by the departure of the charge that these conductors may possess1 but by the advent of opposite charges brought to them by ions which obey the electrostatic attraction and abandon their own electrification when they come in contact with these conductors4 ,this mode of regarding the phenomena is extremely convenient and eminently suggestive4 ,it may1 no doubt1 be thought that the image of the ions is not identical with objective reality1 but we are compelled to acknowledge that it represents with absolute faithfulness all the details of the phenomena4 ,other facts1 moreover1 will give to this hypothesis a still greater value2 we shall even be able1 so to speak1 to grasp these ions individually1 to count them1 and to measure their charge4 #b4 ,,the ,,condensation ,,of ,,water-,,vapour ,,by ,,ions ,if the pressure of a vapour--that of water1 for instance--in the atmosphere reaches the value of the maximum pressure corresponding to the temperature of the experiment1 the elementary theory teaches us that the slightest decrease in temperature will induce a condensation2 that small drops will form1 and the mist will turn into rain4 ,in reality1 matters do not occur in so simple a manner4 ,a more or less considerable delay may take place1 and the vapour will remain supersaturated4 ,we easily discover that this phenomenon is due to the intervention of capillary action4 ,on a drop of liquid a surface-tension takes effect which gives rise to a pressure which becomes greater the smaller the diameter of the drop4 ,pressure facilitates evaporation1 and on more closely examining this reaction we arrive at the conclusion that vapour can never spontaneously condense itself when liquid drops already formed are not present1 unless forces of another nature intervene to diminish the effect of the capillary forces4 ,in the most frequent cases1 these forces come from the dust which is always in suspension in the air1 or which exists in any recipient4 ,grains of dust act by reason of their hygrometrical power1 and form germs round which drops presently form4 ,it is possible to make use1 as did ,m4 ,coulier as early as #ahge1 of this phenomenon to carry off the germs of condensation1 by producing by expansion in a bottle containing a little water a preliminary mist which purifies the air4 ,in subsequent experiments it will be found almost impossible to produce further condensation of vapour4 ,but these forces may also be of electrical origin4 ,von ,helmholtz long since showed that electricity exercises an influence on the condensation of the vapour of water1 and ,mr ,c4,t4,r4 ,wilson1 with this view1 has made truly quantitative experiments4 ,it was rapidly discovered after the apparition of the ,x rays that gases that have become conductors1 that is1 ionised gases1 also facilitate the condensation of supersaturated water vapour4 ,we are thus led by a new road to the belief that electrified centres exist in gases1 and that each centre draws to itself the neighbouring molecules of water1 as an electrified rod of resin does the light bodies around it4 ,there is produced in this manner round each ion an assemblage of molecules of water which constitute a germ capable of causing the formation of a drop of water out of the condensation of excess vapour in the ambient air4 ,as might be expected1 the drops are electrified1 and take to themselves the charge of the centres round which they are formed2 moreover1 as many drops are created as there are ions4 ,thereafter we have only to count these drops to ascertain the number of ions which existed in the gaseous mass4 ,to effect this counting1 several methods have been used1 differing in principle but leading to similar results4 ,it is possible1 as ,mr ,c4,t4,r4 ,wilson and ,professor ,j4,j4 ,thomson have done1 to estimate1 on the one hand1 the weight of the mist which is produced in determined conditions1 and on the other1 the average weight of the drops1 according to the formula formerly given by ,sir ,g4 ,stokes1 by deducting their diameter from the speed with which this mist falls2 or we can1 with ,professor ,lemme1 determine the average radius of the drops by an optical process1 viz4 by measuring the diameter of the first diffraction ring produced when looking through the mist at a point of light4 ,we thus get to a very high number4 ,there are1 for instance1 some twenty million ions per centimetre cube when the rays have produced their maximum effect1 but high as this figure is1 it is still very small compared with the total number of molecules4 ,all conclusions drawn from kinetic theory lead us to think that in the same space there must exist1 by the side of a molecule divided into two ions1 a thousand millions remaining in a neutral state and intact4 ,mr ,c4,t4,r4 ,wilson has remarked that the positive and negative ions do not produce condensation with the same facility4 ,the ions of a contrary sign may be almost completely separated by placing the ionised gas in a suitably disposed field4 ,in the neighbourhood of a negative disk there remain hardly any but positive ions1 and against a positive disk none but negative2 and in effecting a separation of this kind1 it will be noticed that condensation by negative ions is easier than by the positive4 ,it is1 consequently1 possible to cause condensation on negative centres only1 and to study separately the phenomena produced by the two kinds of ions4 ,it can thus be verified that they really bear charges equal in absolute value1 and these charges can even be estimated1 since we already know the number of drops4 ,this estimate can be made1 for example1 by comparing the speed of the fall of a mist in fields of different values1 or1 as did ,j4,j4 ,thomson1 by measuring the total quantity of electricity liberated throughout the gas4 ,at the degree of approximation which such experiments imply1 we find that the charge of a drop1 and consequently the charge borne by an ion1 is sensibly #c4d x #aj-aj electrostatic or #a4a x #aj-bj electromagnetic units4 ,this charge is very near that which the study of the phenomena of ordinary electrolysis leads us to attribute to a univalent atom produced by electrolytic dissociation4 ,such a coincidence is evidently very striking2 but it will not be the only one1 for whatever phenomenon be studied it will always appear that the smallest charge we can conceive as isolated is that mentioned4 ,we are1 in fact1 in presence of a natural unit1 or1 if you will1 of an atom of electricity4 ,we must1 however1 guard against the belief that the gaseous ion is identical with the electrolytic ion4 ,sensible differences between those are immediately apparent1 and still greater ones will be discovered on closer examination4 ,as ,m4 ,perrin has shown1 the ionisation produced by the ,x-rays in no way depends on the chemical composition of the gas2 and whether we take a volume of gaseous hydrochloric acid or a mixture of hydrogen and chlorine in the same condition1 all the results will be identical3 and chemical affinities play no part here4 ,we can also obtain other information regarding ions3 we can ascertain1 for instance1 their velocities1 and also get an idea of their order of magnitude4 ,by treating the speeds possessed by the liberated charges as components of the known speed of a gaseous current1 ,mr ,zeleny measures the mobilities1 that is to say1 the speeds acquired by the positive and negative charges in a field equal to the electrostatic unit4 ,he has thus found that these mobilities are different1 and that they vary1 for example1 between #djj and #bjj centimetres per second for the two charges in dry gases1 the positive being less mobile than the negative ions1 which suggests the idea that they are of greater mass4#cj ,footnote #cj3 ,a full account of these experiments1 which were executed at the ,cavendish ,laboratory1 is to be found in ,philosophical ,transactions1 ,a41 vol4 cxcv4 7#aija71 pp4 #aic et seq4--,,ed4 ,m4 ,langevin1 who has made himself the eloquent apostle of the new doctrines in ,france1 and has done much to make them understood and admitted1 has personally undertaken experiments analogous to those of ,m4 ,zeleny1 but much more complete4 ,he has studied in a very ingenious manner1 not only the mobilities1 but also the law of recombination which regulates the spontaneous return of the gas to its normal state4 ,he has determined experimentally the relation of the number of recombinations to the number of collisions between two ions of contrary sign1 by studying the variation produced by a change in the value of the field1 in the quantity of electricity which can be collected in the gas separating two parallel metallic plates1 after the passage through it for a very short time of the ,rntgen rays emitted during one discharge of a ,crookes tube4 ,if the image of the ions is indeed conformable to reality1 this relation must evidently always be smaller than unity1 and must tend towards this value when the mobility of the ions diminishes1 that is to say1 when the pressure of the gas increases4 ,the results obtained are in perfect accord with this anticipation4 ,on the other hand1 ,m4 ,langevin has succeeded1 by following the displacement of the ions between the parallel plates after the ionisation produced by the radiation1 in determining the absolute values of the mobilities with great precision1 and has thus clearly placed in evidence the irregularity of the mobilities of the positive and negative ions respectively4 ,their mass can be calculated when we know1 through experiments of this kind1 the speed of the ions in a given field1 and on the other hand--as we can now estimate their electric charge--the force which moves them4 ,they evidently progress more slowly the larger they are2 and in the viscous medium constituted by the gas1 the displacement is effected at a speed sensibly proportional to the motive power4 ,at the ordinary temperature these masses are relatively considerable1 and are greater for the positive than for the negative ions1 that is to say1 they are about the order of some ten molecules4 ,the ions1 therefore1 seem to be formed by an agglomeration of neutral molecules maintained round an electrified centre by electrostatic attraction4 ,if the temperature rises1 the thermal agitation will become great enough to prevent the molecules from remaining linked to the centre4 ,by measurements effected on the gases of flames1 we arrive at very different values of the masses from those found for ordinary ions1 and above all1 very different ones for ions of contrary sign4 ,the negative ions have much more considerable velocities than the positive ones4 ,the latter also seem to be of the same size as atoms2 and the first-named must1 consequently1 be considered as very much smaller1 and probably about a thousand times less4 ,thus1 for the first time in science1 the idea appears that the atom is not the smallest fraction of matter to be considered4 ,fragments a thousand times smaller may exist which possess1 however1 a negative charge4 ,these are the electrons1 which other considerations will again bring to our notice4 #c4 ,,how ,,ions ,,are ,,produced ,it is very seldom that a gaseous mass does not contain a few ions4 ,they may have been formed from many causes1 for although to give precision to our studies1 and to deal with a well ascertained case1 ,i mentioned only ionisation by the ,x rays in the first instance1 ,i ought not to give the impression that the phenomenon is confined to these rays4 ,it is1 on the contrary1 very general1 and ionisation is just as well produced by the cathode rays1 by the radiations emitted by radio-active bodies1 by the ultra-violet rays1 by heating to a high temperature1 by certain chemical actions1 and finally by the impact of the ions already existing in neutral molecules4 ,of late years these new questions have been the object of a multitude of researches1 and if it has not always been possible to avoid some confusion1 yet certain general conclusions may be drawn4 ,the ionisation by flames1 in particular1 is fairly well known4 ,for it to be produced spontaneously1 it would appear that there must exist simultaneously a rather high temperature and a chemical action in the gas4 ,according to ,m4 ,moreau1 the ionisation is very marked when the flame contains the vapour of the salt of an alkali or of an alkaline earth1 but much less so when it contains that of other salts4 ,arrhenius1 ,mr ,c4,t4,r4 ,wilson1 and ,m4 ,moreau1 have studied all the circumstances of the phenomenon2 and it seems indeed that there is a somewhat close analogy between what first occurs in the saline vapours and that which is noted in liquid electrolytes4 ,there should be produced1 as soon as a certain temperature is reached1 a dissociation of the saline molecule2 and1 as ,m4 ,moreau has shown in a series of very well conducted researches1 the ions formed at about #ajj;,c4 seem constituted by an electrified centre of the size of a gas molecule1 surrounded by some ten layers of other molecules4 ,we are thus dealing with rather large ions1 but according to ,mr ,wilson1 this condensation phenomenon does not affect the number of ions produced by dissociation4 ,in proportion as the temperature rises1 the molecules condensed round the nucleus disappear1 and1 as in all other circumstances1 the negative ion tends to become an electron1 while the positive ion continues the size of an atom4 ,in other cases1 ions are found still larger than those of saline vapours1 as1 for example1 those produced by phosphorus4 ,it has long been known that air in the neighbourhood of phosphorus becomes a conductor1 and the fact1 pointed out as far back as #ahhe by ,matteucci1 has been well studied by various experimenters1 by ,,mm4 ,elster and ,geitel in #ahij1 for instance4 ,on the other hand1 in #ahic ,mr ,barus established that the approach of a stick of phosphorus brings about the condensation of water vapour1 and we really have before us1 therefore1 in this instance1 an ionisation4 ,m4 ,bloch has succeeded in disentangling the phenomena1 which are here very complex1 and in showing that the ions produced are of considerable dimensions2 for their speed in the same conditions is on the average a thousand times less than that of ions due to the ,x rays4 ,m4 ,bloch has established also that the conductivity of recently-prepared gases1 already studied by several authors1 was analogous to that which is produced by phosphorus1 and that it is intimately connected with the presence of the very tenuous solid or liquid dust which these gases carry with them1 while the ions are of the same order of magnitude4 ,these large ions exist1 moreover1 in small quantities in the atmosphere2 and ,m4 ,langevin lately succeeded in revealing their presence4 ,it may happen1 and this not without singularly complicating matters1 that the ions which were in the midst of material molecules produce1 as the result of collisions1 new divisions in these last4 ,other ions are thus born1 and this production is in part compensated for by recombinations between ions of opposite signs4 ,the impacts will be more active in the event of the gas being placed in a field of force and of the pressure being slight1 the speed attained being then greater and allowing the active force to reach a high value4 ,the energy necessary for the production of an ion is1 in fact1 according to ,professor ,rutherford and ,professor ,stark1 something considerable1 and it much exceeds the analogous force in electrolytic decomposition4 ,it is therefore in tubes of rarefied gas that this ionisation by impact will be particularly felt4 ,this gives us the reason for the aspect presented by ,geissler tubes4 ,generally1 in the case of discharges1 new ions produced by the molecules struck come to add themselves to the electrons produced1 as will be seen1 by the cathode4 ,a full discussion has led to the interpretation of all the known facts1 and to our understanding1 for instance1 why there exist bright or dark spaces in certain regions of the tube4 ,m4 ,pellat1 in particular1 has given some very fine examples of this concordance between the theory and the facts he has skilfully observed4 ,in all the circumstances1 then1 in which ions appear1 their formation has doubtless been provoked by a mechanism analogous to that of the shock4 ,the ,x rays1 if they are attributable to sudden variations in the ether--that is to say1 a variation of the two vectors of ,hertz-- themselves produce within the atom a kind of electric impulse which breaks it into two electrified fragments2 i4e4 the positive centre1 the size of the molecule itself1 and the negative centre1 constituted by an electron a thousand times smaller4 ,round these two centres1 at the ordinary temperature1 are agglomerated by attraction other molecules1 and in this manner the ions whose properties have just been studied are formed4 #d4 ,,electrons ,,in ,,metals ,the success of the ionic hypothesis as an interpretation of the conductivity of electrolytes and gases has suggested the desire to try if a similar hypothesis can represent the ordinary conductivity of metals4 ,we are thus led to conceptions which at first sight seem audacious because they are contrary to our habits of mind4 ,they must not1 however1 be rejected on that account4 ,electrolytic dissociation at first certainly appeared at least as strange2 yet it has ended by forcing itself upon us1 and we could1 at the present day1 hardly dispense with the image it presents to us4 ,the idea that the conductivity of metals is not essentially different from that of electrolytic liquids or gases1 in the sense that the passage of the current is connected with the transport of small electrified particles1 is already of old date4 ,it was enunciated by ,w4 ,weber1 and afterwards developed by ,giese1 but has only obtained its true scope through the effect of recent discoveries4 ,it was the researches of ,riecke1 later1 of ,drude1 and1 above all1 those of ,j4,j4 ,thomson1 which have allowed it to assume an acceptable form4 ,all these attempts are connected however with the general theory of ,lorentz1 which we will examine later4 ,it will be admitted that metallic atoms can1 like the saline molecule in a solution1 partially dissociate themselves4 ,electrons1 very much smaller than atoms1 can move through the structure1 considerable to them1 which is constituted by the atom from which they have just been detached4 ,they may be compared to the molecules of a gas which is enclosed in a porous body4 ,in ordinary conditions1 notwithstanding the great speed with which they are animated1 they are unable to travel long distances1 because they quickly find their road barred by a material atom4 ,they have to undergo innumerable impacts1 which throw them first in one direction and then in another4 ,the passage of a current is a sort of flow of these electrons in a determined direction4 ,this electric flow brings1 however1 no modification to the material medium traversed1 since every electron which disappears at any point is replaced by another which appears at once1 and in all metals the electrons are identical4 ,this hypothesis leads us to anticipate certain facts which experience confirms4 ,thus ,j4,j4 ,thomson shows that if1 in certain conditions1 a conductor is placed in a magnetic field1 the ions have to describe an epicycloid1 and their journey is thus lengthened1 while the electric resistance must increase4 ,if the field is in the direction of the displacement1 they describe helices round the lines of force and the resistance is again augmented1 but in different proportions4 ,various experimenters have noted phenomena of this kind in different substances4 ,for a long time it has been noticed that a relation exists between the calorific and the electric conductivity2 the relation of these two conductivities is sensibly the same for all metals4 ,the modern theory tends to show simply that it must indeed be so4 ,calorific conductivity is due1 in fact1 to an exchange of electrons between the hot and the cold regions1 the heated electrons having the greater velocity1 and consequently the more considerable energy4 ,the calorific exchanges then obey laws similar to those which govern electric exchanges2 and calculation even leads to the exact values which the measurements have given4#ca ,footnote #ca3 ,the whole of this argument is brilliantly set forth by ,professor ,lorentz in a lecture delivered to the ,electrotechnikerverein at ,berlin in ,december #aijd1 and reprinted1 with additions1 in the ,archives ,nerlandaises of #aijf4--;,,ed4 ,in the same way ,professor ,hesehus has explained how contact electrification is produced1 by the tendency of bodies to equalise their superficial properties by means of a transport of electrons1 and ,mr ,jeans has shown that we should discover the existence of the well-known laws of distribution over conducting bodies in electrostatic equilibrium4 ,a metal can1 in fact1 be electrified1 that is to say1 may possess an excess of positive or negative electrons which cannot easily leave it in ordinary conditions4 ,to cause them to do so would need an appreciable amount of work1 on account of the enormous difference of the specific inductive capacities of the metal and of the insulating medium in which it is plunged4 ,electrons1 however1 which1 on arriving at the surface of the metal1 possessed a kinetic energy superior to this work1 might be shot forth and would be disengaged as a vapour escapes from a liquid4 ,now1 the number of these rapid electrons1 at first very slight1 increases1 according to the kinetic theory1 when the temperature rises1 and therefore we must reckon that a wire1 on being heated1 gives out electrons1 that is to say1 loses negative electricity and sends into the surrounding media electrified centres capable of producing the phenomena of ionisation4 ,edison1 in #ahhd1 showed that from the filament of an incandescent lamp there escaped negative electric charges4 ,since then1 ,richardson and ,j4,j4 ,thomson have examined analogous phenomena4 ,this emission is a very general phenomenon which1 no doubt1 plays a considerable part in cosmic physics4 ,professor ,arrhenius explains1 for instance1 the polar auroras by the action of similar corpuscules emitted by the sun4 ,in other phenomena we seem indeed to be confronted by an emission1 not of negative electrons1 but of positive ions4 ,thus1 when a wire is heated1 not in vacuo1 but in a gas1 this wire begins to electrify neighbouring bodies positively4 ,j4,j4 ,thomson has measured the mass of these positive ions and finds it considerable1 i4e4 about #aej times that of an atom of hydrogen4 ,some are even larger1 and constitute almost a real grain of dust4 ,we here doubtless meet with the phenomena of disaggregation undergone by metals at a red heat4 ,,chapter ,,ix ,,cathode ,,rays ,,and ,,radioactive ,,bodies #a4 ,,the ,,cathode ,,rays ,a wire traversed by an electric current is1 as has just been explained1 the seat of a movement of electrons4 ,if we cut this wire1 a flood of electrons1 like a current of water which1 at the point where a pipe bursts1 flows out in abundance1 will appear to spring out between the two ends of the break4 ,if the energy of the electrons is sufficient1 these electrons will in fact rush forth and be propagated in the air or in the insulating medium interposed2 but the phenomena of the discharge will in general be very complex4 ,we shall here only examine a particularly simple case1 viz41 that of the cathode rays2 and without entering into details1 we shall only note the results relating to these rays which furnish valuable arguments in favour of the electronic hypothesis and supply solid materials for the construction of new theories of electricity and matter4 ,for a long time it was noticed that the phenomena in a ,geissler tube changed their aspect considerably1 when the gas pressure became very weak1 without1 however1 a complete vacuum being formed4 ,from the cathode there is shot forth normally and in a straight line a flood within the tube1 dark but capable of impressing a photographic plate1 of developing the fluorescence of various substances 7particularly the glass walls of the tube71 and of producing calorific and mechanical effects4 ,these are the cathode rays1 so named in #ahhc by ,e4 ,wiedemann1 and their name1 which was unknown to a great number of physicists till barely twelve years ago1 has become popular at the present day4 ,about #ahfi1 ,hittorf made an already very complete study of them and put in evidence their principal properties2 but it was the researches of ,sir ,w4 ,crookes in especial which drew attention to them4 ,the celebrated physicist foresaw that the phenomena which were thus produced in rarefied gases were1 in spite of their very great complication1 more simple than those presented by matter under the conditions in which it is generally met with4 ,he devised a celebrated theory no longer admissible in its entirety1 because it is not in complete accord with the facts1 which was1 however1 very interesting1 and contained1 in germ1 certain of our present ideas4 ,in the opinion of ,crookes1 in a tube in which the gas has been rarefied we are in presence of a special state of matter4 ,the number of the gas molecules has become small enough for their independence to be almost absolute1 and they are able in this so-called radiant state to traverse long spaces without departing from a straight line4 ,the cathode rays are due to a kind of molecular bombardment of the walls of the tubes1 and of the screens which can be introduced into them2 and it is the molecules1 electrified by their contact with the cathode and then forcibly repelled by electrostatic action1 which produce1 by their movement and their vis viva1 all the phenomena observed4 ,moreover1 these electrified molecules animated with extremely rapid velocities correspond1 according to the theory verified in the celebrated experiment of ,rowland on convection currents1 to a true electric current1 and can be deviated by a magnet4 ,notwithstanding the success of ,crookes' experiments1 many physicists-- the ,germans especially--did not abandon an hypothesis entirely different from that of radiant matter4 ,they continued to regard the cathode radiation as due to particular radiations of a nature still little known but produced in the luminous ether4 ,this interpretation seemed1 indeed1 in #ahid1 destined to triumph definitely through the remarkable discovery of ,lenard1 a discovery which1 in its turn1 was to provoke so many others and to bring about consequences of which the importance seems every day more considerable4 ,professor ,lenard's fundamental idea was to study the cathode rays under conditions different from those in which they are produced4 ,these rays are born in a very rarefied space1 under conditions perfectly determined by ,sir ,w4 ,crookes2 but it was a question whether1 when once produced1 they would be capable of propagating themselves in other media1 such as a gas at ordinary pressure1 or even in an absolute vacuum4 ,experiment alone could answer this question1 but there were difficulties in the way of this which seemed almost insurmountable4 ,the rays are stopped by glass even of slight thickness1 and how then could the almost vacuous space in which they have to come into existence be separated from the space1 absolutely vacuous or filled with gas1 into which it was desired to bring them8 ,the artifice used was suggested to ,professor ,lenard by an experiment of ,hertz4 ,the great physicist had1 in fact1 shortly before his premature death1 taken up this important question of the cathode rays1 and his genius left there1 as elsewhere1 its powerful impress4 ,he had shown that metallic plates of very slight thickness were transparent to the cathode rays2 and ,professor ,lenard succeeded in obtaining plates impermeable to air1 but which yet allowed the pencil of cathode rays to pass through them4 ,now if we take a ,crookes tube with the extremity hermetically closed by a metallic plate with a slit across the diameter of #a mm4 in width1 and stop this slit with a sheet of very thin aluminium1 it will be immediately noticed that the rays pass through the aluminium and pass outside the tube4 ,they are propagated in air at atmospheric pressure1 and they can also penetrate into an absolute vacuum4 ,they therefore can no longer be attributed to radiant matter1 and we are led to think that the energy brought into play in this phenomenon must have its seat in the light-bearing ether itself4 ,but it is a very strange light which is thus subject to magnetic action1 which does not obey the principle of equal angles1 and for which the most various gases are already disturbed media4 ,according to ,crookes it possesses also the singular property of carrying with it electric charges4 ,this convection of negative electricity by the cathode rays seems quite inexplicable on the hypothesis that the rays are ethereal radiations4 ,nothing then remained in order to maintain this hypothesis1 except to deny the convection1 which1 besides1 was only established by indirect experiments4 ,that the reality of this transport has been placed beyond dispute by means of an extremely elegant experiment which is all the more convincing that it is so very simple1 is due to ,m4 ,perrin4 ,in the interior of a ,crookes tube he collected a pencil of cathode rays in a metal cylinder4 ,according to the elementary principles of electricity the cylinder must become charged with the whole charge1 if there be one1 brought to it by the rays1 and naturally various precautions had to be taken4 ,but the result was very precise1 and doubt could no longer exist--the rays were electrified4 ,it might have been1 and indeed was1 maintained1 some time after this experiment was published1 that while the phenomena were complex inside the tube1 outside1 things might perhaps occur differently4 ,lenard himself1 however1 with that absence of even involuntary prejudice common to all great minds1 undertook to demonstrate that the opinion he at first held could no longer be accepted1 and succeeded in repeating the experiment of ,m4 ,perrin on cathode rays in the air and even in vacuo4 ,on the wrecks of the two contradictory hypotheses thus destroyed1 and out of the materials from which they had been built1 a theory has been constructed which co-ordinates all the known facts4 ,this theory is furthermore closely allied to the theory of ionisation1 and1 like this latter1 is based on the concept of the electron4 ,cathode rays are electrons in rapid motion4 ,the phenomena produced both inside and outside a ,crookes tube are1 however1 generally complex4 ,in ,lenard's first experiments1 and in many others effected later when this region of physics was still very little known1 a few confusions may be noticed even at the present day4 ,at the spot where the cathode rays strike the walls of the tube the essentially different ,x rays appear4 ,these differ from the cathode radiations by being neither electrified nor deviated by a magnet4 ,in their turn these ,x rays may give birth to the secondary rays of ,m4 ,sagnac2 and often we find ourselves in presence of effects from these last-named radiations and not from the true cathode rays4 ,the electrons1 when they are propagated in a gas1 can ionise the molecules of this gas and unite with the neutral atoms to form negative ions1 while positive ions also appear4 ,there are likewise produced1 at the expense of the gas still subsisting after rarefication within the tube1 positive ions which1 attracted by the cathode and reaching it1 are not all neutralised by the negative electrons1 and can1 if the cathode be perforated1 pass through it1 and if not1 pass round it4 ,we have then what are called the canal rays of ,goldstein1 which are deviated by an electric or magnetic field in a contrary direction to the cathode rays2 but1 being larger1 give weak deviations or may even remain undeviated through losing their charge when passing through the cathode4 ,it may also be the parts of the walls at a distance from the cathode which send a positive rush to the latter1 by a similar mechanism4 ,it may be1 again1 that in certain regions of the tube cathode rays are met with diffused by some solid object1 without having thereby changed their nature4 ,all these complexities have been cleared up by ,m4 ,villard1 who has published1 on these questions1 some remarkably ingenious and particularly careful experiments4 ,m4 ,villard has also studied the phenomena of the coiling of the rays in a field1 as already pointed out by ,hittorf and ,plcker4 ,when a magnetic field acts on the cathode particle1 the latter follows a trajectory1 generally helicoidal1 which is anticipated by the theory4 ,we here have to do with a question of ballistics1 and experiments duly confirm the anticipations of the calculation4 ,nevertheless1 rather singular phenomena appear in the case of certain values of the field1 and these phenomena1 dimly seen by ,plcker and ,birkeland1 have been the object of experiments by ,m4 ,villard4 ,the two faces of the cathode seem to emit rays which are deviated in a direction perpendicular to the lines of force by an electric field1 and do not seem to be electrified4 ,m4 ,villard calls them magneto-cathode rays1 and according to ,m4 ,fortin these rays may be ordinary cathode rays1 but of very slight velocity4 ,in certain cases the cathode itself may be superficially disaggregated1 and extremely tenuous particles detach themselves1 which1 being carried off at right angles to its surface1 may deposit themselves like a very thin film on objects placed in their path4 ,various physicists1 among them ,m4 ,houllevigue1 have studied this phenomenon1 and in the case of pressures between #a_/bj and #a_/ajj of a millimetre1 the last-named scholar has obtained mirrors of most metals1 a phenomenon he designates by the name of ionoplasty4 ,but in spite of all these accessory phenomena1 which even sometimes conceal those first observed1 the existence of the electron in the cathodic flux remains the essential characteristic4 ,the electron can be apprehended in the cathodic ray by the study of its essential properties2 and ,j4,j4 ,thomson gave great value to the hypothesis by his measurements4 ,at first he meant to determine the speed of the cathode rays by direct experiment1 and by observing1 in a revolving mirror1 the relative displacement of two bands due to the excitement of two fluorescent screens placed at different distances from the cathode4 ,but he soon perceived that the effect of the fluorescence was not instantaneous1 and that the lapse of time might form a great source of error1 and he then had recourse to indirect methods4 ,it is possible1 by a simple calculation1 to estimate the deviations produced on the rays by a magnetic and an electric field respectively as a function of the speed of propagation and of the relation of the charge to the material mass of the electron4 ,the measurement of these deviations will then permit this speed and this relation to be ascertained4 ,other processes may be used which all give the same two quantities by two suitably chosen measurements4 ,such are the radius of the curve taken by the trajectory of the pencil in a perpendicular magnetic field and the measure of the fall of potential under which the discharge takes place1 or the measure of the total quantity of electricity carried in one second and the measure of the calorific energy which may be given1 during the same period1 to a thermo-electric junction4 ,the results agree as well as can be expected1 having regard to the difficulty of the experiments2 the values of the speed agree also with those which ,professor ,wiechert has obtained by direct measurement4 ,the speed never depends on the nature of the gas contained in the ,crookes tube1 but varies with the value of the fall of potential at the cathode4 ,it is of the order of one tenth of the speed of light1 and it may rise as high as one third4 ,the cathode particle therefore goes about three thousand times faster than the earth in its orbit4 ,the relation is also invariable1 even when the substance of which the cathode is formed is changed or one gas is substituted for another4 ,it is1 on the average1 a thousand times greater than the corresponding relation in electrolysis4 ,as experiment has shown1 in all the circumstances where it has been possible to effect measurements1 the equality of the charges carried by all corpuscules1 ions1 atoms1 etc41 we ought to consider that the charge of the electron is here1 again1 that of a univalent ion in electrolysis1 and therefore that its mass is only a small fraction of that of the atom of hydrogen1 viz41 of the order of about a thousandth part4 ,this is the same result as that to which we were led by the study of flames4 ,the thorough examination of the cathode radiation1 then1 confirms us in the idea that every material atom can be dissociated and will yield an electron much smaller than itself--and always identical whatever the matter whence it comes1--the rest of the atom remaining charged with a positive quantity equal and contrary to that borne by the electron4 ,in the present case these positive ions are no doubt those that we again meet with in the canal rays4 ,professor ,wien has shown that their mass is really1 in fact1 of the order of the mass of atoms4 ,although they are all formed of identical electrons1 there may be various cathode rays1 because the velocity is not exactly the same for all electrons4 ,thus is explained the fact that we can separate them and that we can produce a sort of spectrum by the action of the magnet1 or1 again1 as ,m4 ,deslandres has shown in a very interesting experiment1 by that of an electrostatic field4 ,this also probably explains the phenomena studied by ,m4 ,villard1 and previously pointed out4 #b4 ,,radioactive ,,substances ,even in ordinary conditions1 certain substances called radioactive emit1 quite outside any particular reaction1 radiations complex indeed1 but which pass through fairly thin layers of minerals1 impress photographic plates1 excite fluorescence1 and ionize gases4 ,in these radiations we again find electrons which thus escape spontaneously from radioactive bodies4 ,it is not necessary to give here a history of the discovery of radium1 for every one knows the admirable researches of ,m4 and ,madame ,curie4 ,but subsequent to these first studies1 a great number of facts have accumulated for the last six years1 among which some people find themselves a little lost4 ,it may1 perhaps1 not be useless to indicate the essential results actually obtained4 ,the researches on radioactive substances have their starting-point in the discovery of the rays of uranium made by ,m4 ,becquerel in #ahif4 ,as early as #ahfg ,niepce de ,st ,victor proved that salts of uranium impressed photographic plates in the dark2 but at that time the phenomenon could only pass for a singularity attributable to phosphorescence1 and the valuable remarks of ,niepce fell into oblivion4 ,m4 ,becquerel established1 after some hesitations natural in the face of phenomena which seemed so contrary to accepted ideas1 that the radiating property was absolutely independent of phosphorescence1 that all the salts of uranium1 even the uranous salts which are not phosphorescent1 give similar radiant effects1 and that these phenomena correspond to a continuous emission of energy1 but do not seem to be the result of a storage of energy under the influence of some external radiation4 ,spontaneous and constant1 the radiation is insensible to variations of temperature and light4 ,the nature of these radiations was not immediately understood1#cb and their properties seemed contradictory4 ,this was because we were not dealing with a single category of rays4 ,but amongst all the effects there is one which constitutes for the radiations taken as a whole1 a veritable process for the measurement of radioactivity4 ,this is their ionizing action on gases4 ,a very complete study of the conductivity of air under the influence of rays of uranium has been made by various physicists1 particularly by ,professor ,rutherford1 and has shown that the laws of the phenomenon are the same as those of the ionization due to the action of the ,rntgen rays4 ,footnote #cb3 ,in his work on ,l'volution de la ,matire1 ,m4 ,gustave ,le ,bon recalls that in #ahig he published several notes in the ,acadmie des ,sciences1 in which he asserted that the properties of uranium were only a particular case of a very general law1 and that the radiations emitted did not polarize1 and were akin by their properties to the ,x rays4 ,it was natural to ask one's self if the property discovered in salts of uranium was peculiar to this body1 or if it were not1 to a more or less degree1 a general property of matter4 ,madame ,curie and ,m4 ,schmidt1 independently of each other1 made systematic researches in order to solve the question2 various compounds of nearly all the simple bodies at present known were thus passed in review1 and it was established that radioactivity was particularly perceptible in the compounds of uranium and thorium1 and that it was an atomic property linked to the matter endowed with it1 and following it in all its combinations4 ,in the course of her researches ,madame ,curie observed that certain pitchblendes 7oxide of uranium ore1 containing also barium1 bismuth1 etc47 were four times more active 7activity being measured by the phenomenon of the ionization of the air7 than metallic uranium4 ,now1 no compound containing any other active metal than uranium or thorium ought to show itself more active than those metals themselves1 since the property belongs to their atoms4 ,it seemed1 therefore1 probable that there existed in pitchblendes some substance yet unknown1 in small quantities and more radioactive than uranium4 ,m4 and ,madame ,curie then commenced those celebrated experiments which brought them to the discovery of radium4 ,their method of research has been justly compared in originality and importance to the process of spectrum analysis4 ,to isolate a radioactive substance1 the first thing is to measure the activity of a certain compound suspected of containing this substance1 and this compound is chemically separated4 ,we then again take in hand all the products obtained1 and by measuring their activity anew1 it is ascertained whether the substance sought for has remained in one of these products1 or is divided among them1 and if so1 in what proportion4 ,the spectroscopic reaction which we may use in the course of this separation is a thousand times less sensitive than observation of the activity by means of the electrometer4 ,though the principle on which the operation of the concentration of the radium rests is admirable in its simplicity1 its application is nevertheless very laborious4 ,tons of uranium residues have to be treated in order to obtain a few decigrammes of pure salts of radium4 ,radium is characterised by a special spectrum1 and its atomic weight1 as determined by ,madame ,curie1 is #bbe2 it is consequently the higher homologue of barium in one of the groups of ,mendelef4 ,salts of radium have in general the same chemical properties as the corresponding salts of barium1 but are distinguished from them by the differences of solubility which allow of their separation1 and by their enormous activity1 which is about a hundred thousand times greater than that of uranium4 ,radium produces various chemical and some very intense physiological reactions4 ,its salts are luminous in the dark1 but this luminosity1 at first very bright1 gradually diminishes as the salts get older4 ,we have here to do with a secondary reaction correlative to the production of the emanation1 after which radium undergoes the transformations which will be studied later on4 ,the method of analysis founded by ,m4 and ,madame ,curie has enabled other bodies presenting sensible radioactivity to be discovered4 ,the alkaline metals appear to possess this property in a slight degree4 ,recently fallen snow and mineral waters manifest marked action4 ,the phenomenon may often be due1 however1 to a radioactivity induced by radiations already existing in the atmosphere4 ,but this radioactivity hardly attains the ten-thousandth part of that presented by uranium1 or the ten-millionth of that appertaining to radium4 ,two other bodies1 polonium and actinium1 the one characterised by the special nature of the radiations it emits and the other by a particular spectrum1 seem likewise to exist in pitchblende4 ,these chemical properties have not yet been perfectly defined2 thus ,m4 ,debierne1 who discovered actinium1 has been able to note the active property which seems to belong to it1 sometimes in lanthanum1 sometimes in neodynium4#cc ,it is proved that all extremely radioactive bodies are the seat of incessant transformations1 and even now we cannot state the conditions under which they present themselves in a strictly determined form4 ,footnote #cc3 ,polonium has now been shown to be no new element1 but one of the transformation products of radium4 ,radium itself is also thought to be derived in some manner1 not yet ascertained1 from uranium4 ,the same is the case with actinium1 which is said to come in the long run from uranium1 but not so directly as does radium4 ,all this is described in ,professor ,rutherford's ,radioactive ,transformations 7,london1 #aijf74--;,,ed4 #c4 ,,the ,,radiation ,,of ,,the ,,radioactive ,,bodies ,,and ,,the ,,emanation ,to acquire exact notions as to the nature of the rays emitted by the radioactive bodies1 it was necessary to try to cause magnetic or electric forces to act on them so as to see whether they behaved in the same way as light and the ,x rays1 or whether like the cathode rays they were deviated by a magnetic field4 ,this work was effected by ,professor ,giesel1 then by ,m4 ,becquerel1 ,professor ,rutherford1 and by many other experimenters after them4 ,all the methods which have already been mentioned in principle have been employed in order to discover whether they were electrified1 and1 if so1 by electricity of what sign1 to measure their speed1 and to ascertain their degree of penetration4 ,the general result has been to distinguish three sorts of radiations1 designated by the letters alpha1 beta1 gamma4 ,the alpha rays are positively charged1 and are projected at a speed which may attain the tenth of that of light2 ,m4,h4 ,becquerel has shown by the aid of photography that they are deviated by a magnet1 and ,professor ,rutherford has1 on his side1 studied this deviation by the electrical method4 ,the relation of the charge to the mass is1 in the case of these rays1 of the same order as in that of the ions of electrolysis4 ,they may therefore be considered as exactly analogous to the canal rays of ,goldstein1 and we may attribute them to a material transport of corpuscles of the magnitude of atoms4 ,the relatively considerable size of these corpuscles renders them very absorbable4 ,a flight of a few millimetres in a gas suffices to reduce their number by one-half4 ,they have great ionizing power4 ,the beta rays are on all points similar to the cathode rays2 they are1 as ,m4 and ,madame ,curie have shown1 negatively charged1 and the charge they carry is always the same4 ,their size is that of the electrons1 and their velocity is generally greater than that of the cathode rays1 while it may become almost that of light4 ,they have about a hundred times less ionizing power than the alpha rays4 ,the gamma rays were discovered by ,m4 ,villard4#cd ,they may be compared to the ,x rays2 like the latter1 they are not deviated by the magnetic field1 and are also extremely penetrating4 ,a strip of aluminium five millimetres thick will stop the other kinds1 but will allow them to pass4 ,on the other hand1 their ionizing power is #aj1jjj times less than that of the alpha rays4 ,footnote #cd3 ,this is admitted by ,professor ,rutherford 7,radio-,activity1 ,camb41 #aijd1 p4 #ada7 and ,professor ,soddy 7,radio-,activity1 ,london1 #aijd1 p4 #ff74 ,neither ,mr ,whetham1 in his ,recent ,development of ,physical ,science 7,london1 #aijd7 nor the ,hon4 ,r4,j4 ,strutt in ,the ,becquerel ,rays 7,london1 same date71 both of whom deal with the historical side of the subject1 seem to have noticed the fact4--,,ed4 ,to these radiations there sometimes are added in the course of experiments secondary radiations analogous to those of ,m4 ,sagnac1 and produced when the alpha1 beta1 or gamma rays meet various substances4 ,this complication has often led to some errors of observation4 ,phosphorescence and fluorescence seem especially to result from the alpha and beta rays1 particularly from the alpha rays1 to which belongs the most important part of the total energy of the radiation4 ,sir ,w4 ,crookes has invented a curious little apparatus1 the spinthariscope1 which enables us to examine the phosphorescence of the blende excited by these rays4 ,by means of a magnifying glass1 a screen covered with sulphide of zinc is kept under observation1 and in front of it is disposed1 at a distance of about half a millimetre1 a fragment of some salt of radium4 ,we then perceive multitudes of brilliant points on the screen1 which appear and at once disappear1 producing a scintillating effect4 ,it seems probable that every particle falling on the screen produces by its impact a disturbance in the neighbouring region1 and it is this disturbance which the eye perceives as a luminous point4 ,thus1 says ,sir ,w4 ,crookes1 each drop of rain falling on the surface of still water is not perceived as a drop of rain1 but by reason of the slight splash which it causes at the moment of impact1 and which is manifested by ridges and waves spreading themselves in circles4 ,the various radioactive substances do not all give radiations of identical constitution4 ,radium and thorium possess in somewhat large proportions the three kinds of rays1 and it is the same with actinium4 ,polonium contains especially alpha rays and a few gamma rays4#ce ,in the case of uranium1 the alpha rays have extremely slight penetrating power1 and cannot even impress photographic plates4 ,but the widest difference between the substances proceeds from the emanation4 ,radium1 in addition to the three groups of rays alpha1 beta1 and gamma1 disengages continuously an extremely subtle emanation1 seemingly almost imponderable1 but which may be1 for many reasons1 looked upon as a vapour of which the elastic force is extremely feeble4 ,footnote #ce3 ,it has now been shown that polonium when freshly separated emits beta rays also2 see ,dr ,logeman's paper in ,proceedings of the ,royal ,society1 ,a41 #fth ,september #aijf4--;,,ed4 ,m4 and ,madame ,curie discovered as early as #ahii that every substance placed in the neighbourhood of radium1 itself acquired a radioactivity which persisted for several hours after the removal of the radium4 ,this induced radioactivity seems to be carried to other bodies by the intermediary of a gas4 ,it goes round obstacles1 but there must exist between the radium and the substance a free and continuous space for the activation to take place2 it cannot1 for instance1 do so through a wall of glass4 ,in the case of compounds of thorium ,professor ,rutherford discovered a similar phenomenon2 since then1 various physicists1 ,professor ,soddy1 ,miss ,brooks1 ,miss ,gates1 ,m4 ,danne1 and others1 have studied the properties of these emanations4 ,the substance emanated can neither be weighed nor can its elastic force be ascertained2 but its transformations may be followed1 as it is luminous1 and it is even more certainly characterised by its essential property1 i4e4 its radioactivity4 ,we also see that it can be decanted like a gas1 that it will divide itself between two tubes of different capacity in obedience to the law of ,mariotte1 and will condense in a refrigerated tube in accordance with the principle of ,watt1 while it even complies with the law of ,gay-,lussac4 ,the activity of the emanation vanishes quickly1 and at the end of four days it has diminished by one-half4 ,if a salt of radium is heated1 the emanation becomes more abundant1 and the residue1 which1 however1 does not sensibly diminish in weight1 will have lost all its radioactivity1 and will only recover it by degrees4 ,professor ,rutherford1 notwithstanding many different attempts1 has been unable to make this emanation enter into any chemical reaction4 ,if it be a gaseous body1 it must form part of the argon group1 and1 like its other members1 be perfectly inert4 ,by studying the spectrum of the gas disengaged by a solution of salt of radium1 ,sir ,william ,ramsay and ,professor ,soddy remarked that when the gas is radioactive there are first obtained rays of gases belonging to the argon family1 then by degrees1 as the activity disappears1 the spectrum slowly changes1 and finally presents the characteristic aspect of helium4 ,we know that the existence of this gas was first discovered by spectrum analysis in the sun4 ,later its presence was noted in our atmosphere1 and in a few minerals which happen to be the very ones from which radium has been obtained4 ,it might therefore have been the case that it pre-existed in the gases extracted from radium2 but a remarkable experiment by ,m4 ,curie and ,sir ,james ,dewar seems to show convincingly that this cannot be so4 ,the spectrum of helium never appears at first in the gas proceeding from pure bromide of radium2 but it shows itself1 on the other hand1 very distinctly1 after the radioactive transformations undergone by the salt4 ,all these strange phenomena suggest bold hypotheses1 but to construct them with any solidity they must be supported by the greatest possible number of facts4 ,before admitting a definite explanation of the phenomena which have their seat in the curious substances discovered by them1 ,m4 and ,madame ,curie considered1 with a great deal of reason1 that they ought first to enrich our knowledge with the exact and precise facts relating to these bodies and to the effects produced by the radiations they emit4 ,thus ,m4 ,curie particularly set himself to study the manner in which the radioactivity of the emanation is dissipated1 and the radioactivity that this emanation can induce on all bodies4 ,the radioactivity of the emanation diminishes in accordance with an exponential law4 ,the constant of time which characterises this decrease is easily and exactly determined1 and has a fixed value1 independent of the conditions of the experiment as well as of the nature of the gas which is in contact with the radium and becomes charged with the emanation4 ,the regularity of the phenomenon is so great that it can be used to measure time3 in #cihe seconds#cf the activity is always reduced one-half4 ,footnote #cf3 ,according to ,professor ,rutherford1 in #c4gg days4--,,ed ,radioactivity induced on any body which has been for a long time in presence of a salt of radium disappears more rapidly4 ,the phenomenon appears1 moreover1 more complex1 and the formula which expresses the manner in which the activity diminishes must contain two exponentials4 ,to find it theoretically we have to imagine that the emanation first deposits on the body in question a substance which is destroyed in giving birth to a second1 this latter disappearing in its turn by generating a third4 ,the initial and final substances would be radioactive1 but the intermediary one1 not4 ,if1 moreover1 the bodies acted on are brought to a temperature of over #gjj1 they appear to lose by volatilisation certain substances condensed in them1 and at the same time their activity disappears4 ,the other radioactive bodies behave in a similar way4 ,bodies which contain actinium are particularly rich in emanations4 ,uranium1 on the contrary1 has none4#cg ,this body1 nevertheless1 is the seat of transformations comparable to those which the study of emanations reveals in radium2 ,sir ,w4 ,crookes has separated from uranium a matter which is now called uranium ,x4 ,this matter is at first much more active than its parent1 but its activity diminishes rapidly1 while the ordinary uranium1 which at the time of the separation loses its activity1 regains it by degrees4 ,in the same way1 ,professors ,rutherford and ,soddy have discovered a so-called thorium ,x to be the stage through which ordinary thorium has to pass in order to produce its emanation4#ch ,footnote #cg3 ,professor ,rutherford has lately stated that uranium may possibly produce an emanation1 but that its rate of decay must be too swift for its presence to be verified 7see ,radioactive ,transformations1 p4 #afa74--;,,ed4 ,footnote #ch3 ,an actinium ,x was also discovered by ,professor ,giesel 7,jahrbuch d4 ,radioaktivitat1 i4 p4 #ceh1 #aijd74 ,since the above was written1 another product has been found to intervene between the ,x substance and the emanation in the case of actinium and thorium4 ,they have been named radio-actinium and radio-thorium respectively4--,,ed4 ,it is not possible to give a complete table which should1 as it were1 represent the genealogical tree of the various radioactive substances4 ,several authors have endeavoured to do so1 but in a premature manner2 all the affiliations are not at the present time yet perfectly known1 and it will no doubt be acknowledged some day that identical states have been described under different names4#ci ,footnote #ci3 ,such a table is given on p4 #afi of ,rutherford's ,radioactive ,transformations4--,,ed4 #d4 ,,the ,,disaggregation ,,of ,,matter ,,and ,,atomic ,,energy ,in spite of uncertainties which are not yet entirely removed1 it cannot be denied that many experiments render it probable that in radioactive bodies we find ourselves witnessing veritable transformations of matter4 ,professor ,rutherford1 ,professor ,soddy1 and several other physicists1 have come to regard these phenomena in the following way4 ,a radioactive body is composed of atoms which have little stability1 and are able to detach themselves spontaneously from the parent substance1 and at the same time to divide themselves into two essential component parts1 the negative electron and its residue the positive ion4 ,the first-named constitutes the beta1 and the second the alpha rays4 ,the emanation is certainly composed of alpha ions with a few molecules agglomerated round them4 ,professor ,rutherford has1 in fact1 demonstrated that the emanation is charged with positive electricity2 and this emanation may1 in turn1 be destroyed by giving birth to new bodies4 ,after the loss of the atoms which are carried off by the radiation1 the remainder of the body acquires new properties1 but it may still be radioactive1 and again lose atoms4 ,the various stages that we meet with in the evolution of the radioactive substance or of its emanation1 correspond to the various degrees of atomic disaggregation4 ,professors ,rutherford and ,soddy have described them clearly in the case of uranium and radium4 ,as regards thorium the results are less satisfactory4 ,the evolution should continue until a stable atomic condition is finally reached1 which1 because of this stability1 is no longer radioactive4 ,thus1 for instance1 radium would finally be transformed into helium4#dj ,footnote #dj3 ,this opinion1 no doubt formed when ,sir ,william ,ramsay's discovery of the formation of helium from the radium emanation was first made known1 is now less tenable4 ,the latest theory is that the alpha particle is in fact an atom of helium1 and that the final transformation product of radium and the other radioactive substances is lead4 ,cf4 ,rutherford1 op4 cit4 passim4--,,ed4 ,it is possible1 by considerations analogous to those set forth above in other cases1 to arrive at an idea of the total number of particles per second expelled by one gramme of radium2 ,professor ,rutherford in his most recent evaluation finds that this number approaches #b4e x #ajaa4da ,by calculating from the atomic weight the number of atoms probably contained in this gramme of radium1 and supposing each particle liberated to correspond to the destruction of one atom1 it is found that one half of the radium should disappear in #abhj years2#db and from this we may conceive that it has not yet been possible to discover any sensible loss of weight4 ,sir ,w4 ,ramsay and ,professor ,soddy attained a like result by endeavouring to estimate the mass of the emanation by the quantity of helium produced4 ,footnote #da3 ,see ,radioactive ,transformations 7p4 #bea74 ,professor ,rutherford says that each of the alpha ray products present in one gram of radium product 7sic7 expels #f4b x #ajaj alpha particles per second4 ,he also remarks on the experimental difficulty of accurately determining the number of alpha particles expelled from radium per second4--,,ed4 ,footnote #db3 ,see ,rutherford1 op4 cit4 p4 #aej4--;,,ed4 ,if radium transforms itself in such a way that its activity does not persist throughout the ages1 it loses little by little the provision of energy it had in the beginning1 and its properties furnish no valid argument to oppose to the principle of the conservation of energy4 ,to put everything right1 we have only to recognise that radium possessed in the potential state at its formation a finite quantity of energy which is consumed little by little4 ,in the same manner1 a chemical system composed1 for instance1 of zinc and sulphuric acid1 also contains in the potential state energy which1 if we retard the reaction by any suitable arrangement--such as by amalgamating the zinc and by constituting with its elements a battery which we cause to act on a resistance--may be made to exhaust itself as slowly as one may desire4 ,there can1 therefore1 be nothing in any way surprising in the fact that a combination which1 like the atomic combination of radium1 is not stable--since it disaggregates itself1--is capable of spontaneously liberating energy1 but what may be a little astonishing1 at first sight1 is the considerable amount of this energy4 ,m4 ,curie has calculated directly1 by the aid of the calorimeter1 the quantity of energy liberated1 measuring it entirely in the form of heat4 ,the disengagement of heat accounted for in a grain of radium is uniform1 and amounts to #ajj calories per hour4 ,it must therefore be admitted that an atom of radium1 in disaggregating itself1 liberates #cj1jjj times more energy than a molecule of hydrogen when the latter combines with an atom of oxygen to form a molecule of water4 ,we may ask ourselves how the atomic edifice of the active body can be constructed1 to contain so great a provision of energy4 ,we will remark that such a question might be asked concerning cases known from the most remote antiquity1 like that of the chemical systems1 without any satisfactory answer ever being given4 ,this failure surprises no one1 for we get used to everything--even to defeat4 ,when we come to deal with a new problem we have really no right to show ourselves more exacting2 yet there are found persons who refuse to admit the hypothesis of the atomic disaggregation of radium because they cannot have set before them a detailed plan of that complex whole known to us as an atom4 ,the most natural idea is perhaps the one suggested by comparison with those astronomical phenomena where our observation most readily allows us to comprehend the laws of motion4 ,it corresponds likewise to the tendency ever present in the mind of man1 to compare the infinitely small with the infinitely great4 ,the atom may be regarded as a sort of solar system in which electrons in considerable numbers gravitate round the sun formed by the positive ion4 ,it may happen that certain of these electrons are no longer retained in their orbit by the electric attraction of the rest of the atom1 and may be projected from it like a small planet or comet which escapes towards the stellar spaces4 ,the phenomena of the emission of light compels us to think that the corpuscles revolve round the nucleus with extreme velocities1 or at the rate of thousands of billions of evolutions per second4 ,it is easy to conceive from this that1 notwithstanding its lightness1 an atom thus constituted may possess an enormous energy4#dc ,footnote #dc3 ,this view of the case has been made very clear by ,m4 ,gustave le ,bon in ,l'volution de la ,matire 7,paris1 #aijf74 ,see especially pp4 #cf-eb1 where the amount of the supposed intra-atomic energy is calculated4--,,ed4 ,other authors imagine that the energy of the corpuscles is principally due to the extremely rapid rotations of those elements on their own axes4 ,lord ,kelvin lately drew up on another model the plan of a radioactive atom capable of ejecting an electron with a considerable vis viva4 ,he supposes a spherical atom formed of concentric layers of positive and negative electricity disposed in such a way that its external action is null1 and that1 nevertheless1 the force emanated from the centre may be repellent for certain values when the electron is within it4 ,the most prudent physicists and those most respectful to established principles may1 without any scruples1 admit the explanation of the radioactivity of radium by a dislocation of its molecular edifice4 ,the matter of which it is constituted evolves from an admittedly unstable initial state to another stable one4 ,it is1 in a way1 a slow allotropic transformation which takes place by means of a mechanism regarding which1 in short1 we have no more information than we have regarding other analogous transformations4 ,the only astonishment we can legitimately feel is derived from the thought that we are suddenly and deeply penetrating to the very heart of things4 ,but those persons who have a little more hardihood do not easily resist the temptation of forming daring generalisations4 ,thus it will occur to some that this property1 already discovered in many substances where it exists in more or less striking degree1 is1 with differences of intensity1 common to all bodies1 and that we are thus confronted by a phenomenon derived from an essential quality of matter4 ,quite recently1 ,professor ,rutherford has demonstrated in a fine series of experiments that the alpha particles of radium cease to ionize gases when they are made to lose their velocity1 but that they do not on that account cease to exist4 ,it may follow that many bodies emit similar particles without being easily perceived to do so2 since the electric action1 by which this phenomenon of radioactivity is generally manifested1 would1 in this case1 be but very weak4 ,if we thus believe radioactivity to be an absolutely general phenomenon1 we find ourselves face to face with a new problem4 ,the transformation of radioactive bodies can no longer be assimilated to allotropic transformations1 since thus no final form could ever be attained1 and the disaggregation would continue indefinitely up to the complete dislocation of the atom4#dd ,the phenomenon might1 it is true1 have a duration of perhaps thousands of millions of centuries1 but this duration is but a minute in the infinity of time1 and matters little4 ,our habits of mind1 if we adopt such a conception1 will be none the less very deeply disturbed4 ,we shall have to abandon the idea so instinctively dear to us that matter is the most stable thing in the universe1 and to admit1 on the contrary1 that all bodies whatever are a kind of explosive decomposing with extreme slowness4 ,there is in this1 whatever may have been said1 nothing contrary to any of the principles on which the science of energetics rests2 but an hypothesis of this nature carries with it consequences which ought in the highest degree to interest the philosopher1 and we all know with what alluring boldness ,m4 ,gustave ,le ,bon has developed all these consequences in his work on the evolution of matter4#de ,footnote #dd3 ,this is the main contention of ,m4 ,gustave ,le ,bon in his work last quoted4--,,ed4 ,footnote #de3 ,see last note4--,,ed4 ,there is hardly a physicist who does not at the present day adopt in one shape or another the ballistic hypothesis4 ,all new facts are co-ordinated so happily by it1 that it more and more satisfies our minds2 but it cannot be asserted that it forces itself on our convictions with irresistible weight4 ,another point of view appeared more plausible and simple at the outset1 when there seemed reason to consider the energy radiated by radioactive bodies as inexhaustible4 ,it was thought that the source of this energy was to be looked for without the atom1 and this idea may perfectly well he maintained at the present day4 ,radium on this hypothesis must be considered as a transformer borrowing energy from the external medium and returning it in the form of radiation4 ,it is not impossible1 even1 to admit that the energy which the atom of radium withdraws from the surrounding medium may serve to keep up1 not only the heat emitted and its complex radiation1 but also the dissociation1 supposed to be endothermic1 of this atom4 ,such seems to be the idea of ,m4 ,debierne and also of ,m4 ,sagnac4 ,it does not seem to accord with the experiments that this borrowed energy can be a part of the heat of the ambient medium2 and1 indeed1 such a phenomenon would be contrary to the principle of ,carnot if we wished 7though we have seen how disputable is this extension7 to extend this principle to the phenomena which are produced in the very bosom of the atom4 ,we may also address ourselves to a more noble form of energy1 and ask ourselves whether we are not1 for the first time1 in presence of a transformation of gravitational energy4 ,it may be singular1 but it is not absurd1 to suppose that the unit of mass of radium is not attached to the earth with the same intensity as an inert body4 ,m4 ,sagnac has commenced some experiments1 as yet unpublished1 in order to study the laws of the fall of a fragment of radium4 ,they are necessarily very delicate1 and the energetic and ingenious physicist has not yet succeeded in finishing them4#df ,let us suppose that he succeeds in demonstrating that the intensity of gravity is less for radium than for the platinum or the copper of which the pendulums used to illustrate the law of ,newton are generally made2 it would then be possible still to think that the laws of universal attraction are perfectly exact as regards the stars1 and that ponderability is really a particular case of universal attraction1 while in the case of radioactive bodies part of the gravitational energy is transformed in the course of its evolution and appears in the form of active radiation4 ,footnote #df3 ,in reality ,m4 ,sagnac operated in the converse manner4 ,he took two equal weights of a salt of radium and a salt of barium1 which he made oscillate one after the other in a torsion balance4 ,had the durations of oscillation been different1 it might be concluded that the mechanical mass is not the same for radium as for barium4 ,but for this explanation to be admitted1 it would evidently need to be supported by very numerous facts4 ,it might1 no doubt1 appear still more probable that the energy borrowed from the external medium by radium is one of those still unknown to us1 but of which a vague instinct causes us to suspect the existence around us4 ,it is indisputable1 moreover1 that the atmosphere in all directions is furrowed with active radiations2 those of radium may be secondary radiations reflected by a kind of resonance phenomenon4 ,certain experiments by ,professors ,elster and ,geitel1 however1 are not favourable to this point of view4 ,if an active body be surrounded by a radioactive envelope1 a screen should prevent this body from receiving any impression from outside1 and yet there is no diminution apparent in the activity presented by a certain quantity of radium when it is lowered to a depth of #hjj metres under ground1 in a region containing a notable quantity of pitchblende4 ,these negative results are1 on the other hand1 so many successes for the partisans of the explanation of radioactivity by atomic energy4 ,,chapter ,x ,,the ,,ether ,,and ,,matter #a4 ,,the ,,relations ,,between ,,the ,,ether ,,and ,,matter ,for some time past it has been the more or less avowed ambition of physicists to construct with the particles of ether all possible forms of corporeal existence2 but our knowledge of the inmost nature of things has hitherto seemed too limited for us to attempt such an enterprise with any chance of success4 ,the electronic hypothesis1 however1 which has furnished a satisfactory image of the most curious phenomena produced in the bosom of matter1 has also led to a more complete electromagnetic theory of the ether than that of ,maxwell1 and this twofold result has given birth to the hope of arriving by means of this hypothesis at a complete co-ordination of the physical world4 ,the phenomena whose study may bring us to the very threshold of the problem1 are those in which the connections between matter and the ether appear clearly and in a relatively simple manner4 ,thus in the phenomena of emission1 ponderable matter is seen to give birth to waves which are transmitted by the ether1 and by the phenomena of absorption it is proved that these waves disappear and excite modifications in the interior of the material bodies which receive them4 ,we here catch in operation actual reciprocal actions and reactions between the ether and matter4 ,if we could thoroughly comprehend these actions1 we should no doubt be in a position to fill up the gap which separates the two regions separately conquered by physical science4 ,in recent years numerous researches have supplied valuable materials which ought to be utilized by those endeavouring to construct a theory of radiation4 ,we are1 perhaps1 still ill informed as to the phenomena of luminescence in which undulations are produced in a complex manner1 as in the case of a stick of moist phosphorus which is luminescent in the dark1 or in that of a fluorescent screen4 ,but we are very well acquainted with emission or absorption by incandescence1 where the only transformation is that of calorific into radiating energy1 or vice versa4 ,it is in this case alone that can be correctly applied the celebrated demonstration by which ,kirchhoff established1 by considerations borrowed from thermodynamics1 the proportional relations between the power of emission and that of absorption4 ,in treating of the measurement of temperature1 ,i have already pointed out the experiments of ,professors ,lummer and ,pringsheim and the theoretical researches of ,stephan and ,professor ,wien4 ,we may consider that at the present day the laws of the radiation of dark bodies are tolerably well known1 and1 in particular1 the manner in which each elementary radiation increases with the temperature4 ,a few doubts1 however1 subsist with respect to the law of the distribution of energy in the spectrum4 ,in the case of real and solid bodies the results are naturally less simple than in that of dark bodies4 ,one side of the question has been specially studied on account of its great practical interest1 that is to say1 the fact that the relation of the luminous energy to the total amount radiated by a body varies with the nature of this last2 and the knowledge of the conditions under which this relation becomes most considerable led to the discovery of incandescent lighting by gas in the ,auer-,welsbach mantle1 and to the substitution for the carbon thread in the electric light bulb of a filament of osmium or a small rod of magnesium1 as in the ,nernst lamp4 ,careful measurements effected by ,m4 ,fery have furnished1 in particular1 important information on the radiation of the white oxides2 but the phenomena noticed have not yet found a satisfactory interpretation4 ,moreover1 the radiation of calorific origin is here accompanied by a more or less important luminescence1 and the problem becomes very complex4 ,in the same way that1 for the purpose of knowing the constitution of matter1 it first occurred to us to investigate gases1 which appear to be molecular edifices built on a more simple and uniform plan than solids1 we ought naturally to think that an examination of the conditions in which emission and absorption are produced by gaseous bodies might be eminently profitable1 and might perhaps reveal the mechanism by which the relations between the molecule of the ether and the molecule of matter might be established4 ,unfortunately1 if a gas is not absolutely incapable of emitting some sort of rays by simple heat1 the radiation thus produced1 no doubt by reason of the slightness of the mass in play1 always remains of moderate intensity4 ,in nearly all the experiments1 new energies of chemical or electrical origin come into force4 ,on incandescence1 luminescence is superposed2 and the advantage which might have been expected from the simplicity of the medium vanishes through the complication of the circumstances in which the phenomenon is produced4 ,professor ,pringsheim has succeeded1 in certain cases1 in finding the dividing line between the phenomena of luminescence and that of incandescence4 ,thus the former takes a predominating importance when the gas is rendered luminous by electrical discharges1 and chemical transformations1 especially1 play a preponderant rle in the emission of the spectrum of flames which contain a saline vapour4 ,in all the ordinary experiments of spectrum analysis the laws of ,kirchhoff cannot therefore be considered as established1 and yet the relation between emission and absorption is generally tolerably well verified4 ,no doubt we are here in presence of a kind of resonance phenomenon1 the gaseous atoms entering into vibration when solicited by the ether by a motion identical with the one they are capable of communicating to it4 ,if we are not yet very far advanced in the study of the mechanism of the production of the spectrum1#dg we are1 on the other hand1 well acquainted with its constitution4 ,the extreme confusion which the spectra of the lines of the gases seemed to present is now1 in great part at least1 cleared up4 ,balmer gave some time since1 in the case of the hydrogen spectrum1 an empirical formula which enabled the rays discovered later by an eminent astronomer1 ,m4 ,deslandres1 to be represented2 but since then1 both in the cases of line and band spectra1 the labours of ,professor ,rydberg1 of ,m4 ,deslandres1 of ,professors ,kayzer and ,runge1 and of ,m4 ,thiele1 have enabled us to comprehend1 in their smallest details1 the laws of the distribution of lines and bands4 ,footnote #dg3 ,many theories as to the cause of the lines and bands of the spectrum have been put forward since this was written1 among which that of ,professor ,stark 7for which see ,physikalische ,zeitschrift for #aijf1 passim7 is perhaps the most advanced4 ,that of ,m4 ,jean ,becquerel1 which would attribute it to the vibration within the atom of both negative and positive electrons1 also deserves notice4 ,a popular account of this is given in the ,athenum of #bjth ,april #aijg4--;,,ed4 ,these laws are simple1 but somewhat singular4 ,the radiations emitted by a gas cannot be compared to the notes to which a sonorous body gives birth1 nor even to the most complicated vibrations of any elastic body4 ,the number of vibrations of the different rays are not the successive multiples of one and the same number1 and it is not a question of a fundamental radiation and its harmonics1 while--and this is an essential difference--the number of vibrations of the radiation tend towards a limit when the period diminishes infinitely instead of constantly increasing1 as would be the case with the vibrations of sound4 ,thus the assimilation of the luminous to the elastic vibration is not correct4 ,once again we find that the ether does not behave like matter which obeys the ordinary laws of mechanics1 and every theory must take full account of these curious peculiarities which experiment reveals4 ,another difference1 likewise very important1 between the luminous and the sonorous vibrations1 which also points out how little analogous can be the constitutions of the media which transmit the vibrations1 appears in the phenomena of dispersion4 ,the speed of propagation1 which1 as we have seen when discussing the measurement of the velocity of sound1 depends very little on the musical note1 is not at all the same in the case of the various radiations which can be propagated in the same substance4 ,the index of refraction varies with the duration of the period1 or1 if you will1 with the length of wave in vacuo which is proportioned to this duration1 since in vacuo the speed of propagation is entirely the same for all vibrations4 ,cauchy was the first to propose a theory on which other attempts have been modelled2 for example1 the very interesting and simple one of ,briot4 ,this last-named supposed that the luminous vibration could not perceptibly drag with it the molecular material of the medium across which it is propagated1 but that matter1 nevertheless1 reacts on the ether with an intensity proportional to the elongation1 in such a manner as tends to bring it back to its position of equilibrium4 ,with this simple hypothesis we can fairly well interpret the phenomena of the dispersion of light in the case of transparent substances2 but far from well1 as ,m4 ,carvallo has noted in some extremely careful experiments1 the dispersion of the infra-red spectrum1 and not at all the peculiarities presented by absorbent substances4 ,m4 ,boussinesq arrives at almost similar results1 by attributing dispersion1 on the other hand1 to the partial dragging along of ponderable matter and to its action on the ether4 ,by combining1 in a measure1 as was subsequently done by ,m4 ,boussinesq1 the two hypotheses1 formulas can be established far better in accord with all the known facts4 ,these facts are somewhat complex4 ,it was at first thought that the index always varied in inverse ratio to the wave-length1 but numerous substances have been discovered which present the phenomenon of abnormal dispersion--that is to say1 substances in which certain radiations are propagated1 on the contrary1 the more quickly the shorter their period4 ,this is the case with gases themselves1 as demonstrated1 for example1 by a very elegant experiment of ,m4 ,becquerel on the dispersion of the vapour of sodium4 ,moreover1 it may happen that yet more complications may be met with1 as no substance is transparent for the whole extent of the spectrum4 ,in the case of certain radiations the speed of propagation becomes nil1 and the index shows sometimes a maximum and sometimes a minimum4 ,all those phenomena are in close relation with those of absorption4 ,it is1 perhaps1 the formula proposed by ,helmholtz which best accounts for all these peculiarities4 ,helmholtz came to establish this formula by supposing that there is a kind of friction between the ether and matter1 which1 like that exercised on a pendulum1 here produces a double effect1 changing1 on the one hand1 the duration of this oscillation1 and1 on the other1 gradually damping it4 ,he further supposed that ponderable matter is acted on by elastic forces4 ,the theory of ,helmholtz has the great advantage of representing1 not only the phenomena of dispersion1 but also1 as ,m4 ,carvallo has pointed out1 the laws of rotatory polarization1 its dispersion and other phenomena1 among them the dichroism of the rotatory media discovered by ,m4 ,cotton4 ,in the establishment of these theories1 the language of ordinary optics has always been employed4 ,the phenomena are looked upon as due to mechanical deformations or to movements governed by certain forces4 ,the electromagnetic theory leads1 as we have seen1 to the employment of other images4 ,m4,h4 ,poincar1 and1 after him1 ,helmholtz1 have both proposed electromagnetic theories of dispersion4 ,on examining things closely1 it will be found that there are not1 in truth1 in the two ways of regarding the problem1 two equivalent translations of exterior reality4 ,the electrical theory gives us to understand1 much better than the mechanical one1 that in vacuo the dispersion ought to be strictly null1 and this absence of dispersion appears to be confirmed with extraordinary precision by astronomical observations4 ,thus the observation1 often repeated1 and at different times of year1 proves that in the case of the star ,algol1 the light of which takes at least four years to reach us1 no sensible difference in coloration accompanies the changes in brilliancy4 #b4 ,,the ,,theory ,,of ,,lorentz ,purely mechanical considerations have therefore failed to give an entirely satisfactory interpretation of the phenomena in which even the simplest relations between matter and the ether appear4 ,they would1 evidently1 be still more insufficient if used to explain certain effects produced on matter by light1 which could not1 without grave difficulties1 be attributed to movement2 for instance1 the phenomena of electrification under the influence of certain radiations1 or1 again1 chemical reactions such as photographic impressions4 ,the problem had to be approached by another road4 ,the electromagnetic theory was a step in advance1 but it comes to a standstill1 so to speak1 at the moment when the ether penetrates into matter4 ,if we wish to go deeper into the inwardness of the phenomena1 we must follow1 for example1 ,professor ,lorentz or ,dr ,larmor1 and look with them for a mode of representation which appears1 besides1 to be a natural consequence of the fundamental ideas forming the basis of ,hertz's experiments4 ,the moment we look upon a wave in the ether as an electromagnetic wave1 a molecule which emits light ought to be considered as a kind of excitant4 ,we are thus led to suppose that in each radiating molecule there are one or several electrified particles1 animated with a to-and-fro movement round their positions of equilibrium1 and these particles are certainly identical with those electrons the existence of which we have already admitted for so many other reasons4 ,in the simplest theory1 we will imagine an electron which may be displaced from its position of equilibrium in all directions1 and is1 in this displacement1 submitted to attractions which communicate to it a vibration like a pendulum4 ,these movements are equivalent to tiny currents1 and the mobile electron1 when animated with a considerable velocity1 must be sensitive to the action of the magnet which modifies the form of the trajectory and the value of the period4 ,this almost direct consequence was perceived by ,lorentz1 and it led him to the new idea that radiations emitted by a body ought to be modified by the action of a strong electromagnet4 ,an experiment enabled this prevision to be verified4 ,it was made1 as is well known1 as early as #ahif by ,zeeman2 and the discovery produced a legitimate sensation4 ,when a flame is subjected to the action of a magnetic field1 a brilliant line is decomposed in conditions more or less complex which an attentive study1 however1 allows us to define4 ,according to whether the observation is made in a plane normal to the magnetic field or in the same direction1 the line transforms itself into a triplet or doublet1 and the new lines are polarized rectilinearly or circularly4 ,these are the precise phenomena which the calculation foretells3 the analysis of the modifications undergone by the light supplies1 moreover1 valuable information on the electron itself4 ,from the direction of the circular vibrations of the greatest frequency we can determine the sign of the electric charge in motion and we find it to be negative4 ,but1 further than this1 from the variation of the period we can calculate the relation of the force acting on the electron to its material mass1 and1 in addition1 the relation of the charge to the mass4 ,we then find for this relation precisely that value which we have already met with so many times4 ,such a coincidence cannot be fortuitous1 and we have the right to believe that the electron revealed by the luminous wave which emanates from it1 is really the same as the one made known to us by the study of the cathode rays and of the radioactive substances4 ,however1 the elementary theory does not suffice to interpret the complications which later experiments have revealed4 ,the physicists most qualified to effect measurements in these delicate optical questions--,m4 ,cornu1 ,mr ,preston1 ,m4 ,cotton1 ,,mm4 ,becquerel and ,deslandres1 ,m4 ,broca1 ,professor ,michelson1 and others--have pointed out some remarkable peculiarities4 ,thus in some cases the number of the component rays dissociated by the magnetic field may be very considerable4 ,the great modification brought to a radiation by the ,zeeman effect may1 besides1 combine itself with other phenomena1 and alter the light in a still more complicated manner4 ,a pencil of polarized light1 as demonstrated by ,signori ,macaluzo and ,corbino1 undergoes1 in a magnetic field1 modifications with regard to absorption and speed of propagation4 ,some ingenious researches by ,m4 ,becquerel and ,m4 ,cotton have perfectly elucidated all these complications from an experimental point of view4 ,it would not be impossible to link together all these phenomena without adopting the electronic hypothesis1 by preserving the old optical equations as modified by the terms relating to the action of the magnetic field4 ,this has actually been done in some very remarkable work by ,m4 ,voigt1 but we may also1 like ,professor ,lorentz1 look for more general theories1 in which the essential image of the electrons shall be preserved1 and which will allow all the facts revealed by experiment to be included4 ,we are thus led to the supposition that there is not in the atom one vibrating electron only1 but that there is to be found in it a dynamical system comprising several material points which may be subjected to varied movements4 ,the neutral atom may therefore be considered as composed of an immovable principal portion positively charged1 round which move1 like satellites round a planet1 several negative electrons of very inferior mass4 ,this conclusion leads us to an interpretation in agreement with that which other phenomena have already suggested4 ,these electrons1 which thus have a variable velocity1 generate around themselves a transverse electromagnetic wave which is propagated with the velocity of light2 for the charged particle becomes1 as soon as it experiences a change of speed1 the centre of a radiation4 ,thus is explained the phenomenon of the emission of radiations4 ,in the same way1 the movement of electrons may be excited or modified by the electrical forces which exist in any pencil of light they receive1 and this pencil may yield up to them a part of the energy it is carrying4 ,this is the phenomenon of absorption4 ,professor ,lorentz has not contented himself with thus explaining all the mechanism of the phenomena of emission and absorption4 ,he has endeavoured to rediscover1 by starting with the fundamental hypothesis1 the quantitative laws discovered by thermodynamics4 ,he succeeds in showing that1 agreeably to the law of ,kirchhoff1 the relation between the emitting and the absorbing power must be independent of the special properties of the body under observation1 and he thus again meets with the laws of ,planck and of ,wien3 unfortunately the calculation can only be made in the case of great wave-lengths1 and grave difficulties exist4 ,thus it cannot be very clearly explained why1 by heating a body1 the radiation is displaced towards the side of the short wave-lengths1 or1 if you will1 why a body becomes luminous from the moment its temperature has reached a sufficiently high degree4 ,on the other hand1 by calculating the energy of the vibrating particles we are again led to attribute to these particles the same constitution as that of the electrons4 ,it is in the same way possible1 as ,professor ,lorentz has shown1 to give a very satisfactory explanation of the thermo-electric phenomena by supposing that the number of liberated electrons which exist in a given metal at a given temperature has a determined value varying with each metal1 and is1 in the case of each body1 a function of the temperature4 ,the formula obtained1 which is based on these hypotheses1 agrees completely with the classic results of ,clausius and of ,lord ,kelvin4 ,finally1 if we recollect that the phenomena of electric and calorific conductivity are perfectly interpreted by the hypothesis of electrons1 it will no longer be possible to contest the importance of a theory which allows us to group together in one synthesis so many facts of such diverse origins4 ,if we study the conditions under which a wave excited by an electron's variations in speed can be transmitted1 they again bring us face to face1 and generally1 with the results pointed out by the ordinary electromagnetic theory4 ,certain peculiarities1 however1 are not absolutely the same4 ,thus the theory of ,lorentz1 as well as that of ,maxwell1 leads us to foresee that if an insulating mass be caused to move in a magnetic field normally to its lines of force1 a displacement will be produced in this mass analogous to that of which ,faraday and ,maxwell admitted the existence in the dielectric of a charged condenser4 ,but ,m4,h4 ,poincar has pointed out that1 according as we adopt one or other of these authors' points of view1 so the value of the displacement differs4 ,this remark is very important1 for it may lead to an experiment which would enable us to make a definite choice between the two theories4 ,to obtain the displacement estimated according to ,lorentz1 we must multiply the displacement calculated according to ,hertz by a factor representing the relation between the difference of the specific inductive capacities of the dielectric and of a vacuum1 and the first of these powers4 ,if therefore we take as dielectric the air of which the specific inductive capacity is perceptibly the same as that of a vacuum1 the displacement1 according to the idea of ,lorentz1 will be null2 while1 on the contrary1 according to ,hertz1 it will have a finite value4 ,m4 ,blondlot has made the experiment4 ,he sent a current of air into a condenser placed in a magnetic field1 and was never able to notice the slightest trace of electrification4 ,no displacement1 therefore1 is effected in the dielectric4 ,the experiment being a negative one1 is evidently less convincing than one giving a positive result1 but it furnishes a very powerful argument in favour of the theory of ,lorentz4 ,this theory1 therefore1 appears very seductive1 yet it still raises objections on the part of those who oppose to it the principles of ordinary mechanics4 ,if we consider1 for instance1 a radiation emitted by an electron belonging to one material body1 but absorbed by another electron in another body1 we perceive immediately that1 the propagation not being instantaneous1 there can be no compensation between the action and the reaction1 which are not simultaneous2 and the principle of ,newton thus seems to be attacked4 ,in order to preserve its integrity1 it has to be admitted that the movements in the two material substances are compensated by that of the ether which separates these substances2 but this conception1 although in tolerable agreement with the hypothesis that the ether and matter are not of different essence1 involves1 on a closer examination1 suppositions hardly satisfactory as to the nature of movements in the ether4 ,for a long time physicists have admitted that the ether as a whole must be considered as being immovable and capable of serving1 so to speak1 as a support for the axes of ,galileo1 in relation to which axes the principle of inertia is applicable1--or better still1 as ,m4 ,painlev has shown1 they alone allow us to render obedience to the principle of causality4 ,but if it were so1 we might apparently hope1 by experiments in electromagnetism1 to obtain absolute motion1 and to place in evidence the translation of the earth relatively to the ether4 ,but all the researches attempted by the most ingenious physicists towards this end have always failed1 and this tends towards the idea held by many geometricians that these negative results are not due to imperfections in the experiments1 but have a deep and general cause4 ,now ,lorentz has endeavoured to find the conditions in which the electromagnetic theory proposed by him might agree with the postulate of the complete impossibility of determining absolute motion4 ,it is necessary1 in order to realise this concord1 to imagine that a mobile system contracts very slightly in the direction of its translation to a degree proportioned to the square of the ratio of the velocity of transport to that of light4 ,the electrons themselves do not escape this contraction1 although the observer1 since he participates in the same motion1 naturally cannot notice it4 ,lorentz supposes1 besides1 that all forces1 whatever their origin1 are affected by a translation in the same way as electromagnetic forces4 ,m4 ,langevin and ,m4 ,h4 ,poincar have studied this same question and have noted with precision various delicate consequences of it4 ,the singularity of the hypotheses which we are thus led to construct in no way constitutes an argument against the theory of ,lorentz2 but it has1 we must acknowledge1 discouraged some of the more timid partisans of this theory4#dh ,footnote #dh3 ,an objection not here noticed has lately been formulated with much frankness by ,professor ,lorentz himself4 ,it is one of the pillars of his theory that only the negative electrons move when an electric current passes through a metal1 and that the positive electrons 7if any such there be7 remain motionless4 ,yet in the experiment known as ,hall's1 the current is deflected by the magnetic field to one side of the strip in certain metals1 and to the opposite side in others4 ,this seems to show that in certain cases the positive electrons move instead of the negative1 and ,professor ,lorentz confesses that up to the present he can find no valid argument against this4 ,see ,archives ,nerlandaises #aijf1 parts #a and #b4--;,,ed4 #c4 ,,the ,,mass ,,of ,,electrons ,other conceptions1 bolder still1 are suggested by the results of certain interesting experiments4 ,the electron affords us the possibility of considering inertia and mass to be no longer a fundamental notion1 but a consequence of the electromagnetic phenomena4 ,professor ,j4,j4 ,thomson was the first to have the clear idea that a part1 at least1 of the inertia of an electrified body is due to its electric charge4 ,this idea was taken up and precisely stated by ,professor ,max ,abraham1 who1 for the first time1 was led to regard seriously the seemingly paradoxical notion of mass as a function of velocity4 ,consider a small particle bearing a given electric charge1 and let us suppose that this particle moves through the ether4 ,it is1 as we know1 equivalent to a current proportional to its velocity1 and it therefore creates a magnetic field the intensity of which is likewise proportional to its velocity3 to set it in motion1 therefore1 there must be communicated to it over and above the expenditure corresponding to the acquisition of its ordinary kinetic energy1 a quantity of energy proportional to the square of its velocity4 ,everything1 therefore1 takes place as if1 by the fact of electrification1 its capacity for kinetic energy and its material mass had been increased by a certain constant quantity4 ,to the ordinary mass may be added1 if you will1 an electromagnetic mass4 ,this is the state of things so long as the speed of the translation of the particle is not very great1 but they are no longer quite the same when this particle is animated with a movement whose rapidity becomes comparable to that with which light is propagated4 ,the magnetic field created is then no longer a field in repose1 but its energy depends1 in a complicated manner1 on the velocity1 and the apparent increase in the mass of the particle itself becomes a function of the velocity4 ,more than this1 this increase may not be the same for the same velocity1 but varies according to whether the acceleration is parallel with or perpendicular to the direction of this velocity4 ,in other words1 there seems to be a longitudinal2 and a transversal mass which need not be the same4 ,all these results would persist even if the material mass were very small relatively to the electromagnetic mass2 and the electron possesses some inertia even if its ordinary mass becomes slighter and slighter4 ,the apparent mass1 it can be easily shown1 increases indefinitely when the velocity with which the electrified particle is animated tends towards the velocity of light1 and thus the work necessary to communicate such a velocity to an electron would be infinite4 ,it is in consequence impossible that the speed of an electron1 in relation to the ether1 can ever exceed1 or even permanently attain to1 #cjj1jjj kilometres per second4 ,all the facts thus predicted by the theory are confirmed by experiment4 ,there is no known process which permits the direct measurement of the mass of an electron1 but it is possible1 as we have seen1 to measure simultaneously its velocity and the relation of the electric charge to its mass4 ,in the case of the cathode rays emitted by radium1 these measurements are particularly interesting1 for the reason that the rays which compose a pencil of cathode rays are animated by very different speeds1 as is shown by the size of the stain produced on a photographic plate by a pencil of them at first very constricted and subsequently dispersed by the action of an electric or magnetic field4 ,professor ,kaufmann has effected some very careful experiments by a method he terms the method of crossed spectra1 which consists in superposing the deviations produced by a magnetic and an electric field respectively acting in directions at right angles one to another4 ,he has thus been enabled by working in vacuo to register the very different velocities which1 starting in the case of certain rays from about seven-tenths of the velocity of light1 attain in other cases to ninety-five hundredths of it4 ,it is thus noted that the ratio of charge to mass--which for ordinary speeds is constant and equal to that already found by so many experiments--diminishes slowly at first1 and then very rapidly when the velocity of the ray increases and approaches that of light4 ,if we represent this variation by a curve1 the shape of this curve inclines us to think that the ratio tends toward zero when the velocity tends towards that of light4 ,all the earlier experiments have led us to consider that the electric charge was the same for all electrons1 and it can hardly be conceived that this charge can vary with the velocity4 ,for in order that the relation1 of which one of the terms remains fixed1 should vary1 the other term necessarily cannot remain constant4 ,the experiments of ,professor ,kaufmann1 therefore1 confirm the previsions of ,max ,abraham's theory3 the mass depends on the velocity1 and increases indefinitely in proportion as this velocity approaches that of light4 ,these experiments1 moreover1 allow the numerical results of the calculation to be compared with the values measured4 ,this very satisfactory comparison shows that the apparent total mass is sensibly equal to the electromagnetic mass2 the material mass of the electron is therefore nil1 and the whole of its mass is electromagnetic4 ,thus the electron must be looked upon as a simple electric charge devoid of matter4 ,previous examination has led us to attribute to it a mass a thousand times less that that of the atom of hydrogen1 and a more attentive study shows that this mass was fictitious4 ,the electromagnetic phenomena which are produced when the electron is set in motion or a change effected in its velocity1 simply have the effect1 as it were1 of simulating inertia1 and it is the inertia due to the charge which has caused us to be thus deluded4 ,the electron is therefore simply a small volume determined at a point in the ether1 and possessing special properties2#di this point is propagated with a velocity which cannot exceed that of light4 ,when this velocity is constant1 the electron creates around it in its passage an electric and a magnetic field2 round this electrified centre there exists a kind of wake1 which follows it through the ether and does not become modified so long as the velocity remains invariable4 ,if other electrons follow the first within a wire1 their passage along the wire will be what is called an electric current4 ,footnote #di3 ,this cannot be said to be yet completely proved4 ,cf4 ,sir ,oliver ,lodge1 ,electrons1 ,london1 #aijf1 p4 #bjj4--;,,ed4 ,when the electron is subjected to an acceleration1 a transverse wave is produced1 and an electromagnetic radiation is generated1 of which the character may naturally change with the manner in which the speed varies4 ,if the electron has a sufficiently rapid periodical movement1 this wave is a light wave2 while if the electron stops suddenly1 a kind of pulsation is transmitted through the ether1 and thus we obtain ,rntgen rays4 #d4 ,,new ,,views ,,on ,,the ,,constitution ,,of ,,the ,,ether ,,and ,,of ,,matter ,new and valuable information is thus afforded us regarding the properties of the ether1 but will this enable us to construct a material representation of this medium which fills the universe1 and so to solve a problem which has baffled1 as we have seen1 the prolonged efforts of our predecessors8 ,certain scholars seem to have cherished this hope4 ,dr4 ,larmor in particular1 as we have seen1 has proposed a most ingenious image1 but one which is manifestly insufficient4 ,the present tendency of physicists rather tends to the opposite view2 since they consider matter as a very complex object1 regarding which we wrongly imagine ourselves to be well informed because we are so much accustomed to it1 and its singular properties end by seeming natural to us4 ,but in all probability the ether is1 in its objective reality1 much more simple1 and has a better right to be considered as fundamental4 ,we cannot therefore1 without being very illogical1 define the ether by material properties1 and it is useless labour1 condemned beforehand to sterility1 to endeavour to determine it by other qualities than those of which experiment gives us direct and exact knowledge4 ,the ether is defined when we know1 in all its points1 and in magnitude and in direction1 the two fields1 electric and magnetic1 which may exist in it4 ,these two fields may vary2 we speak from habit of a movement propagated in the ether1 but the phenomenon within the reach of experiment is the propagation of these variations4 ,since the electrons1 considered as a modification of the ether symmetrically distributed round a point1 perfectly counterfeit that inertia which is the fundamental property of matter1 it becomes very tempting to suppose that matter itself is composed of a more or less complex assemblage of electrified centres in motion4 ,this complexity is1 in general1 very great1 as is demonstrated by the examination of the luminous spectra produced by the atoms1 and it is precisely because of the compensations produced between the different movements that the essential properties of matter--the law of the conservation of inertia1 for example--are not contrary to the hypothesis4 ,the forces of cohesion thus would be due to the mutual attractions which occur in the electric and magnetic fields produced in the interior of bodies2 and it is even conceivable that there may be produced1 under the influence of these actions1 a tendency to determine orientation1 that is to say1 that a reason can be seen why matter may be crystallised4#ej ,footnote #ej3 ,the reader should1 however1 be warned that a theory has lately been put forth which attempts to account for crystallisation on purely mechanical grounds4 ,see ,messrs ,barlow and ,pope's ,development of the ,atomic ,theory in the ,transactions of the ,chemical ,society1 #aijf4--;,,ed4 ,all the experiments effected on the conductivity of gases or metals1 and on the radiations of active bodies1 have induced us to regard the atom as being constituted by a positively charged centre having practically the same magnitude as the atom itself1 round which the electrons gravitate2 and it might evidently be supposed that this positive centre itself preserves the fundamental characteristics of matter1 and that it is the electrons alone which no longer possess any but electromagnetic mass4 ,we have but little information concerning these positive particles1 though they are met with in an isolated condition1 as we have seen1 in the canal rays or in the ,x rays4#ea ,it has not hitherto been possible to study them so successfully as the electrons themselves2 but that their magnitude causes them to produce considerable perturbations in the bodies on which they fall is manifest by the secondary emissions which complicate and mask the primitive phenomenon4 ,there are1 however1 strong reasons for thinking that these positive centres are not simple4 ,thus ,professor ,stark attributes to them1 with experiments in proof of his opinion1 the emission of the spectra of the rays in ,geissler tubes1 and the complexity of the spectrum discloses the complexity of the centre4 ,besides1 certain peculiarities in the conductivity of metals cannot be explained without a supposition of this kind4 ,so that the atom1 deprived of the cathode corpuscle1 would be still liable to decomposition into elements analogous to electrons and positively charged4 ,consequently nothing prevents us supposing that this centre likewise simulates inertia by its electromagnetic properties1 and is but a condition localised in the ether4 ,footnote #ea3 ,there is much reason for thinking that the canal rays do not contain positive particles alone1 but are accompanied by negative electrons of slow velocity4 ,the ,x rays are thought1 as has been said above1 to contain neither negative nor positive particles1 but to be merely pulses in the ether4--,,ed4 ,however this may be1 the edifice thus constructed1 being composed of electrons in periodical motion1 necessarily grows old4 ,the electrons become subject to accelerations which produce a radiation towards the exterior of the atom2 and certain of them may leave the body1 while the primitive stability is1 in the end1 no longer assured1 and a new arrangement tends to be formed4 ,matter thus seems to us to undergo those transformations of which the radio-active bodies have given us such remarkable examples4 ,we have already had1 in fragments1 these views on the constitution of matter2 a deeper study of the electron thus enables us to take up a position from which we obtain a sharp1 clear1 and comprehensive grasp of the whole and a glimpse of indefinite horizons4 ,it would be advantageous1 however1 in order to strengthen this position1 that a few objections which still menace it should be removed4 ,the instability of the electron is not yet sufficiently demonstrated4 ,how is it that its charge does not waste itself away1 and what bonds assure the permanence of its constitution8 ,on the other hand1 the phenomena of gravitation remain a mystery4 ,lorentz has endeavoured to build up a theory in which he explains attraction by supposing that two charges of similar sign repel each other in a slightly less degree than that in which two charges1 equal but of contrary sign1 attract each other1 the difference being1 however1 according to the calculation1 much too small to be directly observed4 ,he has also sought to explain gravitation by connecting it with the pressures which may be produced on bodies by the vibratory movements which form very penetrating rays4 ,recently ,m4 ,sutherland has imagined that attraction is due to the difference of action in the convection currents produced by the positive and negative corpuscles which constitute the atoms of the stars1 and are carried along by the astronomical motions4 ,but these hypotheses remain rather vague1 and many authors think1 like ,m4 ,langevin1 that gravitation must result from some mode of activity of the ether totally different from the electromagnetic mode4 ,,chapter ,,xi ,,the ,,future ,,of ,,physics ,it would doubtless be exceedingly rash1 and certainly very presumptuous1 to seek to predict the future which may be reserved for physics4 ,the rle of prophet is not a scientific one1 and the most firmly established previsions of to-day may be overthrown by the reality of to-morrow4 ,nevertheless1 the physicist does not shun an extrapolation of some little scope when it is not too far from the realms of experiment2 the knowledge of the evolution accomplished of late years authorises a few suppositions as to the direction in which progress may continue4 ,the reader who has deigned to follow me in the rapid excursion we have just made through the domain of the science of ,nature1 will doubtless bring back with him from his short journey the general impression that the ancient limits to which the classic treatises still delight in restricting the divers chapters of physics1 are trampled down in all directions4 ,the fine straight roads traced out by the masters of the last century1 and enlarged and levelled by the labour of such numbers of workmen1 are now joined together by a crowd of small paths which furrow the field of physics4 ,it is not only because they cover regions as yet little explored where discoveries are more abundant and more easy1 that these cross-cuts are so frequent1 but also because a higher hope guides the seekers who engage in these new routes4 ,in spite of the repeated failures which have followed the numerous attempts of past times1 the idea has not been abandoned of one day conquering the supreme principle which must command the whole of physics4 ,some physicists1 no doubt1 think such a synthesis to be impossible of realisation1 and that ,nature is infinitely complex2 but1 notwithstanding all the reserves they may make1 from the philosophical point of view1 as to the legitimacy of the process1 they do not hesitate to construct general hypotheses which1 in default of complete mental satisfaction1 at least furnish them with a highly convenient means of grouping an immense number of facts till then scattered abroad4 ,their error1 if error there be1 is beneficial1 for it is one of those that ,kant would have classed among the fruitful illusions which engender the indefinite progress of science and lead to great and important co-ordinations4 ,it is1 naturally1 by the study of the relations existing between phenomena apparently of very different orders that there can be any hope of reaching the goal2 and it is this which justifies the peculiar interest accorded to researches effected in the debatable land between domains hitherto considered as separate4 ,among all the theories lately proposed1 that of the ions has taken a preponderant place2 ill understood at first by some1 appearing somewhat singular1 and in any case useless1 to others1 it met at its inception1 in ,france at least1 with only very moderate favour4 ,to-day things have greatly changed1 and those even who ignored it have been seduced by the curious way in which it adapts itself to the interpretation of the most recent experiments on very different subjects4 ,a very natural reaction has set in2 and ,i might almost say that a question of fashion has led to some exaggerations4 ,the electron has conquered physics1 and many adore the new idol rather blindly4 ,certainly we can only bow before an hypothesis which enables us to group in the same synthesis all the discoveries on electric discharges and on radioactive substances1 and which leads to a satisfactory theory of optics and of electricity2 while by the intermediary of radiating heat it seems likely to embrace shortly the principles of thermodynamics also4 ,certainly one must admire the power of a creed which penetrates also into the domain of mechanics and furnishes a simple representation of the essential properties of matter2 but it is right not to lose sight of the fact that an image may be a well-founded appearance1 but may not be capable of being exactly superposed on the objective reality4 ,the conception of the atom of electricity1 the foundation of the material atoms1 evidently enables us to penetrate further into ,nature's secrets than our predecessors2 but we must not be satisfied with words1 and the mystery is not solved when1 by a legitimate artifice1 the difficulty has simply been thrust further back4 ,we have transferred to an element ever smaller and smaller those physical qualities which in antiquity were attributed to the whole of a substance2 and then we shifted them later to those chemical atoms which1 united together1 constitute this whole4 ,to-day we pass them on to the electrons which compose these atoms4 ,the indivisible is thus rendered1 in a way1 smaller and smaller1 but we are still unacquainted with what its substance may be4 ,the notion of an electric charge which we substitute for that of a material mass will permit phenomena to be united which we thought separate1 but it cannot be considered a definite explanation1 or as the term at which science must stop4 ,it is probable1 however1 that for a few years still physics will not travel beyond it4 ,the present hypothesis suffices for grouping known facts1 and it will doubtless enable many more to be foreseen1 while new successes will further increase its possessions4 ,then the day will arrive when1 like all those which have shone before it1 this seductive hypothesis will lead to more errors than discoveries4 ,it will1 however1 have been improved1 and it will have become a very vast and very complete edifice which some will not willingly abandon2 for those who have made to themselves a comfortable dwelling-place on the ruins of ancient monuments are often too loth to leave it4 ,in that day the searchers who were in the van of the march after truth will be caught up and even passed by others who will have followed a longer1 but perhaps surer road4 ,we also have seen at work those prudent physicists who dreaded too daring creeds1 and who sought only to collect all the documentary evidence possible1 or only took for their guide a few principles which were to them a simple generalisation of facts established by experiments2 and we have been able to prove that they also were effecting good and highly useful work4 ,neither the former nor the latter1 however1 carry out their work in an isolated way1 and it should be noted that most of the remarkable results of these last years are due to physicists who have known how to combine their efforts and to direct their activity towards a common object1 while perhaps it may not be useless to observe also that progress has been in proportion to the material resources of our laboratories4 ,it is probable that in the future1 as in the past1 the greatest discoveries1 those which will suddenly reveal totally unknown regions1 and open up entirely new horizons1 will be made by a few scholars of genius who will carry on their patient labour in solitary meditation1 and who1 in order to verify their boldest conceptions1 will no doubt content themselves with the most simple and least costly experimental apparatus4 ,yet for their discoveries to yield their full harvest1 for the domain to be systematically worked and desirable results obtained1 there will be more and more required the association of willing minds1 the solidarity of intelligent scholars1 and it will be also necessary for these last to have at their disposal the most delicate as well as the most powerful instruments4 ,these are conditions paramount at the present day for continuous progress in experimental science4 ,if1 as has already happened1 unfortunately1 in the history of science1 these conditions are not complied with2 if the freedoms of the workers are trammelled1 their unity disturbed1 and if material facilities are too parsimoniously afforded them1--evolution1 at present so rapid1 may be retarded1 and those retrogressions which1 by-the-by1 have been known in all evolutions1 may occur1 although even then hope in the future would not be abolished for ever4 ,there are no limits to progress1 and the field of our investigations has no boundaries4 ,evolution will continue with invincible force4 ,what we to-day call the unknowable1 will retreat further and further before science1 which will never stay her onward march4 ,thus physics will give greater and increasing satisfaction to the mind by furnishing new interpretations of phenomena2 but it will accomplish1 for the whole of society1 more valuable work still1 by rendering1 by the improvements it suggests1 life every day more easy and more agreeable1 and by providing mankind with weapons against the hostile forces of ,nature4