Calculation has enabled M. Van der Waals, by the application of his kinetic theories, and M. Duhem, by means of thermodynamics, to foresee most of the results which have since been verified by experiment. All these facts have been admirably set forth and systematically co-ordinated by M. Mathias, who, by his own researches, moreover, has made contributions of the highest value to the study of questions regarding the continuity of the liquid and gaseous states.

The further knowledge of critical elements has allowed the laws of corresponding states to be more closely examined in the case of homogeneous substances. It has shown that, as I have already said, bodies must be arranged in groups, and this fact clearly proves that the properties of a given fluid are not determined by its critical constants alone, and that it is necessary to add to them some other specific parameters; M. Mathias and M. D. Berthelot have indicated some which seem to play a considerable part.

It results also from this that the characteristic equation of a fluid cannot yet be considered perfectly known. Neither the equation of Van der Waals nor the more complicated formulas which have been proposed by various authors are in perfect conformity with reality. We may think that researches of this kind will only be successful if attention is concentrated, not only on the phenomena of compressibility and dilatation, but also on the calorimetric properties of bodies. Thermodynamics indeed establishes relations between those properties and other constants, but does not allow everything to be foreseen.

Several physicists have effected very interesting calorimetric measurements, either, like M. Perot, in order to verify Clapeyron's formula regarding the heat of vaporization, or to ascertain the values of specific heats and their variations when the temperature or the pressure happens to change. M. Mathias has even succeeded in completely determining the specific heats of liquefied gases and of their saturated vapours, as well as the heat of internal and external vaporization.

Sec. 2. THE LIQUEFACTION OF GASES, AND THE PROPERTIES OF BODIES AT A LOW TEMPERATURE

The scientific advantages of all these researches have been great, and, as nearly always happens, the practical consequences derived from them have also been most important. It is owing to the more complete knowledge of the general properties of fluids that immense progress has been made these last few years in the methods of liquefying gases.

From a theoretical point of view the new processes of liquefaction can be classed in two categories. Linde's machine and those resembling it utilize, as is known, expansion without any notable production of external work. This expansion, nevertheless, causes a fall in the temperature, because the gas in the experiment is not a perfect gas, and, by an ingenious process, the refrigerations produced are made cumulative.

Several physicists have proposed to employ a method whereby liquefaction should be obtained by expansion with recuperable external work. This method, proposed as long ago as 1860 by Siemens, would offer considerable advantages. Theoretically, the liquefaction would be more rapid, and obtained much more economically; but unfortunately in the experiment serious obstacles are met with, especially from the difficulty of obtaining a suitable lubricant under intense cold for those parts of the machine which have to be in movement if the apparatus is to work.

M. Claude has recently made great progress on this point by the use, during the running of the machine, of the ether of petrol, which is uncongealable, and a good lubricant for the moving parts. When once the desired region of cold is reached, air itself is used, which moistens the metals but does not completely avoid friction; so that the results would have remained only middling, had not this ingenious physicist devised a new improvement which has some analogy with superheating of steam in steam engines. He slightly varies the initial temperature of the compressed air on the verge of liquefaction so as to avoid a zone of deep perturbations in the properties of fluids, which would make the work of expansion very feeble and the cold produced consequently slight. This improvement, simple as it is in appearance, presents several other advantages which immediately treble the output.

The special object of M. Claude was to obtain oxygen in a practical manner by the actual distillation of liquid air. Since nitrogen boils at -194 deg. and oxygen at -180.5 deg. C., if liquid air be evaporated, the nitrogen escapes, especially at the commencement of the evaporation, while the oxygen concentrates in the residual liquid, which finally consists of pure oxygen, while at the same time the temperature rises to the boiling-point (-180.5 deg. C.) of oxygen. But liquid air is costly, and if one were content to evaporate it for the purpose of collecting a part of the oxygen in the residuum, the process would have a very poor result from the commercial point of view. As early as 1892, Mr Parkinson thought of improving the output by recovering the cold produced by liquid air during its evaporation; but an incorrect idea, which seems to have resulted from certain experiments of Dewar—the idea that the phenomenon of the liquefaction of air would not be, owing to certain peculiarities, the exact converse of that of vaporization—led to the employment of very imperfect apparatus. M. Claude, however, by making use of a method which he calls the reversal[8] method, obtains a complete rectification in a remarkably simple manner and under extremely advantageous economic conditions. Apparatus, of surprisingly reduced dimensions but of great efficiency, is now in daily work, which easily enables more than a thousand cubic metres of oxygen to be obtained at the rate, per horse-power, of more than a cubic metre per hour.

[Footnote 8: Methode avec retour en arriere.—ED]

It is in England, thanks to the skill of Sir James Dewar and his pupils—thanks also, it must be said, to the generosity of the Royal Institution, which has devoted considerable sums to these costly experiments—that the most numerous and systematic researches have been effected on the production of intense cold. I shall here note only the more important results, especially those relating to the properties of bodies at low temperatures.

Their electrical properties, in particular, undergo some interesting modifications. The order which metals assume in point of conductivity is no longer the same as at ordinary temperatures. Thus at -200 deg. C. copper is a better conductor than silver. The resistance diminishes with the temperature, and, down to about -200 deg., this diminution is almost linear, and it would seem that the resistance tends towards zero when the temperature approaches the absolute zero. But, after -200 deg., the pattern of the curves changes, and it is easy to foresee that at absolute zero the resistivities of all metals would still have, contrary to what was formerly supposed, a notable value. Solidified electrolytes which, at temperatures far below their fusion point, still retain a very appreciable conductivity, become, on the contrary, perfect insulators at low temperatures. Their dielectric constants assume relatively high values. MM. Curie and Compan, who have studied this question from their own point of view, have noted, moreover, that the specific inductive capacity changes considerably with the temperature.

In the same way, magnetic properties have been studied. A very interesting result is that found in oxygen: the magnetic susceptibility of this body increases at the moment of liquefaction. Nevertheless, this increase, which is enormous (since the susceptibility becomes sixteen hundred times greater than it was at first), if we take it in connection with equal volumes, is much less considerable if taken in equal masses. It must be concluded from this fact that the magnetic properties apparently do not belong to the molecules themselves, but depend on their state of aggregation.

The mechanical properties of bodies also undergo important modifications. In general, their cohesion is greatly increased, and the dilatation produced by slight changes of temperature is considerable. Sir James Dewar has effected careful measurements of the dilatation of certain bodies at low temperatures: for example, of ice. Changes in colour occur, and vermilion and iodide of mercury pass into pale orange. Phosphorescence becomes more intense, and most bodies of complex structure—milk, eggs, feathers, cotton, and flowers—become phosphorescent. The same is the case with certain simple bodies, such as oxygen, which is transformed into ozone and emits a white light in the process.

Chemical affinity is almost put an end to; phosphorus and potassium remain inert in liquid oxygen. It should, however, be noted, and this remark has doubtless some interest for the theories of photographic action, that photographic substances retain, even at the temperature of liquid hydrogen, a very considerable part of their sensitiveness to light.

Sir James Dewar has made some important applications of low temperatures in chemical analysis; he also utilizes them to create a vacuum. His researches have, in fact, proved that the pressure of air congealed by liquid hydrogen cannot exceed the millionth of an atmosphere. We have, then, in this process, an original and rapid means of creating an excellent vacuum in apparatus of very different kinds—a means which, in certain cases, may be particularly convenient.[9]

[Footnote 9: Professor Soddy, in a paper read before the Royal Society on the 15th November 1906, warns experimenters against vacua created by charcoal cooled in liquid air (the method referred-to in the text), unless as much of the air as possible is first removed with a pump and replaced by some argon-free gas. According to him, neither helium nor argon is absorbed by charcoal. By the use of electrically-heated calcium, he claims to have produced an almost perfect vacuum.—ED.]

Thanks to these studies, a considerable field has been opened up for biological research, but in this, which is not our subject, I shall notice one point only. It has been proved that vital germs—bacteria, for example—may be kept for seven days at -190 deg.C. without their vitality being modified. Phosphorescent organisms cease, it is true, to shine at the temperature of liquid air, but this fact is simply due to the oxidations and other chemical reactions which keep up the phosphorescence being then suspended, for phosphorescent activity reappears so soon as the temperature is again sufficiently raised. An important conclusion has been drawn from these experiments which affects cosmogonical theories: since the cold of space could not kill the germs of life, it is in no way absurd to suppose that, under proper conditions, a germ may be transmitted from one planet to another.

Among the discoveries made with the new processes, the one which most strikingly interested public attention is that of new gases in the atmosphere. We know how Sir William Ramsay and Dr. Travers first observed by means of the spectroscope the characteristics of the companions of argon in the least volatile part of the atmosphere. Sir James Dewar on the one hand, and Sir William Ramsay on the other, subsequently separated in addition to argon and helium, crypton, xenon, and neon. The process employed consists essentially in first solidifying the least volatile part of the air and then causing it to evaporate with extreme slowness. A tube with electrodes enables the spectrum of the gas in process of distillation to be observed. In this manner, the spectra of the various gases may be seen following one another in the inverse order of their volatility. All these gases are monoatomic, like mercury; that is to say, they are in the most simple state, they possess no internal molecular energy (unless it is that which heat is capable of supplying), and they even seem to have no chemical energy. Everything leads to the belief that they show the existence on the earth of an earlier state of things now vanished. It may be supposed, for instance, that helium and neon, of which the molecular mass is very slight, were formerly more abundant on our planet; but at an epoch when the temperature of the globe was higher, the very speed of their molecules may have reached a considerable value, exceeding, for instance, eleven kilometres per second, which suffices to explain why they should have left our atmosphere. Crypton and neon, which have a density four times greater than oxygen, may, on the contrary, have partly disappeared by solution at the bottom of the sea, where it is not absurd to suppose that considerable quantities would be found liquefied at great depths.[10]

[Footnote 10: Another view, viz. that these inert gases are a kind of waste product of radioactive changes, is also gaining ground. The discovery of the radioactive mineral malacone, which gives off both helium and argon, goes to support this. See Messrs Ketchin and Winterson's paper on the subject at the Chemical Society, 18th October 1906.—ED.]

It is probable, moreover, that the higher regions of the atmosphere are not composed of the same air as that around us. Sir James Dewar points out that Dalton's law demands that every gas composing the atmosphere should have, at all heights and temperatures, the same pressure as if it were alone, the pressure decreasing the less quickly, all things being equal, as its density becomes less. It results from this that the temperature becoming gradually lower as we rise in the atmosphere, at a certain altitude there can no longer remain any traces of oxygen or nitrogen, which no doubt liquefy, and the atmosphere must be almost exclusively composed of the most volatile gases, including hydrogen, which M.A. Gautier has, like Lord Rayleigh and Sir William Ramsay, proved to exist in the air. The spectrum of the Aurora borealis, in which are found the lines of those parts of the atmosphere which cannot be liquefied in liquid hydrogen, together with the lines of argon, crypton, and xenon, is quite in conformity with this point of view. It is, however, singular that it should be the spectrum of crypton, that is to say, of the heaviest gas of the group, which appears most clearly in the upper regions of the atmosphere.

Among the gases most difficult to liquefy, hydrogen has been the object of particular research and of really quantitative experiments. Its properties in a liquid state are now very clearly known. Its boiling-point, measured with a helium thermometer which has been compared with thermometers of oxygen and hydrogen, is -252 deg.; its critical temperature is -241 deg. C.; its critical pressure, 15 atmospheres. It is four times lighter than water, it does not present any absorption spectrum, and its specific heat is the greatest known. It is not a conductor of electricity. Solidified at 15 deg. absolute, it is far from reminding one by its aspect of a metal; it rather resembles a piece of perfectly pure ice, and Dr Travers attributes to it a crystalline structure. The last gas which has resisted liquefaction, helium, has recently been obtained in a liquid state; it appears to have its boiling-point in the neighbourhood of 6 deg. absolute.[11]

[Footnote 11: M. Poincare is here in error. Helium has never been liquefied.—ED.]

Sec. 3. SOLIDS AND LIQUIDS

The interest of the results to which the researches on the continuity between the liquid and the gaseous states have led is so great, that numbers of scholars have naturally been induced to inquire whether something analogous might not be found in the case of liquids and solids. We might think that a similar continuity ought to be there met with, that the universal character of the properties of matter forbade all real discontinuity between two different states, and that, in truth, the solid was a prolongation of the liquid state.

To discover whether this supposition is correct, it concerns us to compare the properties of liquids and solids. If we find that all properties are common to the two states we have the right to believe, even if they presented themselves in different degrees, that, by a continuous series of intermediary bodies, the two classes might yet be connected. If, on the other hand, we discover that there exists in these two classes some quality of a different nature, we must necessarily conclude that there is a discontinuity which nothing can remove.

The distinction established, from the point of view of daily custom, between solids and liquids, proceeds especially from the difficulty that we meet with in the one case, and the facility in the other, when we wish to change their form temporarily or permanently by the action of mechanical force. This distinction only corresponds, however, in reality, to a difference in the value of certain coefficients. It is impossible to discover by this means any absolute characteristic which establishes a separation between the two classes. Modern researches prove this clearly. It is not without use, in order to well understand them, to state precisely the meaning of a few terms generally rather loosely employed.

If a conjunction of forces acting on a homogeneous material mass happens to deform it without compressing or dilating it, two very distinct kinds of reactions may appear which oppose themselves to the effort exercised. During the time of deformation, and during that time only, the first make their influence felt. They depend essentially on the greater or less rapidity of the deformation, they cease with the movement, and could not, in any case, bring the body back to its pristine state of equilibrium. The existence of these reactions leads us to the idea of viscosity or internal friction.

The second kind of reactions are of a different nature. They continue to act when the deformation remains stationary, and, if the external forces happen to disappear, they are capable of causing the body to return to its initial form, provided a certain limit has not been exceeded. These last constitute rigidity.

At first sight a solid body appears to have a finite rigidity and an infinite viscosity; a liquid, on the contrary, presents a certain viscosity, but no rigidity. But if we examine the matter more closely, beginning either with the solids or with the liquids, we see this distinction vanish.

Tresca showed long ago that internal friction is not infinite in a solid; certain bodies can, so to speak, at once flow and be moulded. M.W. Spring has given many examples of such phenomena. On the other hand, viscosity in liquids is never non-existent; for were it so for water, for example, in the celebrated experiment effected by Joule for the determination of the mechanical equivalent of the caloric, the liquid borne along by the floats would slide without friction on the surrounding liquid, and the work done by movement would be the same whether the floats did or did not plunge into the liquid mass.

In certain cases observed long ago with what are called pasty bodies, this viscosity attains a value almost comparable to that observed by M. Spring in some solids. Nor does rigidity allow us to establish a barrier between the two states. Notwithstanding the extreme mobility of their particles, liquids contain, in fact, vestiges of the property which we formerly wished to consider the special characteristic of solids.

Maxwell before succeeded in rendering the existence of this rigidity very probable by examining the optical properties of a deformed layer of liquid. But a Russian physicist, M. Schwedoff, has gone further, and has been able by direct experiments to show that a sheath of liquid set between two solid cylinders tends, when one of the cylinders is subjected to a slight rotation, to return to its original position, and gives a measurable torsion to a thread upholding the cylinder. From the knowledge of this torsion the rigidity can be deduced. In the case of a solution containing 1/2 per cent. of gelatine, it is found that this rigidity, enormous compared with that of water, is still, however, one trillion eight hundred and forty billion times less than that of steel.

This figure, exact within a few billions, proves that the rigidity is very slight, but exists; and that suffices for a characteristic distinction to be founded on this property. In a general way, M. Spring has also established that we meet in solids, in a degree more or less marked, with the properties of liquids. When they are placed in suitable conditions of pressure and time, they flow through orifices, transmit pressure in all directions, diffuse and dissolve one into the other, and react chemically on each other. They may be soldered together by compression; by the same means alloys may be produced; and further, which seems to clearly prove that matter in a solid state is not deprived of all molecular mobility, it is possible to realise suitable limited reactions and equilibria between solid salts, and these equilibria obey the fundamental laws of thermodynamics.

Thus the definition of a solid cannot be drawn from its mechanical properties. It cannot be said, after what we have just seen, that solid bodies retain their form, nor that they have a limited elasticity, for M. Spring has made known a case where the elasticity of solids is without any limit.

It was thought that in the case of a different phenomenon—that of crystallization—we might arrive at a clear distinction, because here we should he dealing with a specific quality; and that crystallized bodies would be the true solids, amorphous bodies being at that time regarded as liquids viscous in the extreme.

But the studies of a German physicist, Professor O. Lehmann, seem to prove that even this means is not infallible. Professor Lehmann has succeeded, in fact, in obtaining with certain organic compounds— oleate of potassium, for instance—under certain conditions some peculiar states to which he has given the name of semi-fluid and liquid crystals. These singular phenomena can only be observed and studied by means of a microscope, and the Carlsruhe Professor had to devise an ingenious apparatus which enabled him to bring the preparation at the required temperature on to the very plate of the microscope.

It is thus made evident that these bodies act on polarized light in the manner of a crystal. Those that M. Lehmann terms semi-liquid still present traces of polyhedric delimitation, but with the peaks and angles rounded by surface-tension, while the others tend to a strictly spherical form. The optical examination of the first-named bodies is very difficult, because appearances may be produced which are due to the phenomena of refraction and imitate those of polarization. For the other kind, which are often as mobile as water, the fact that they polarize light is absolutely unquestionable.

Unfortunately, all these liquids are turbid, and it may be objected that they are not homogeneous. This want of homogeneity may, according to M. Quincke, be due to the existence of particles suspended in a liquid in contact with another liquid miscible with it and enveloping it as might a membrane, and the phenomena of polarization would thus be quite naturally explained.[12]

[Footnote 12: Professor Quincke's last hypothesis is that all liquids on solidifying pass through a stage intermediate between solid and liquid, in which they form what he calls "foam-cells," and assume a viscous structure resembling that of jelly. See Proc. Roy. Soc. A., 23rd July 1906.—ED.]

M. Tamman is of opinion that it is more a question of an emulsion, and, on this hypothesis, the action on light would actually be that which has been observed. Various experimenters have endeavoured of recent years to elucidate this question. It cannot be considered absolutely settled, but these very curious experiments, pursued with great patience and remarkable ingenuity, allow us to think that there really exist certain intermediary forms between crystals and liquids in which bodies still retain a peculiar structure, and consequently act on light, but nevertheless possess considerable plasticity.

Let us note that the question of the continuity of the liquid and solid states is not quite the same as the question of knowing whether there exist bodies intermediate in all respects between the solids and liquids. These two problems are often wrongly confused. The gap between the two classes of bodies may be filled by certain substances with intermediate properties, such as pasty bodies and bodies liquid but still crystallized, because they have not yet completely lost their peculiar structure. Yet the transition is not necessarily established in a continuous fashion when we are dealing with the passage of one and the same determinate substance from the liquid to the solid form. We conceive that this change may take place by insensible degrees in the case of an amorphous body. But it seems hardly possible to consider the case of a crystal, in which molecular movements must be essentially regular, as a natural sequence to the case of the liquid where we are, on the contrary, in presence of an extremely disordered state of movement.

M. Tamman has demonstrated that amorphous solids may very well, in fact, be regarded as superposed liquids endowed with very great viscosity. But it is no longer the same thing when the solid is once in the crystallized state. There is then a solution of continuity of the various properties of the substance, and the two phases may co-exist.

We might presume also, by analogy with what happens with liquids and gases, that if we followed the curve of transformation of the crystalline into the liquid phase, we might arrive at a kind of critical point at which the discontinuity of their properties would vanish.

Professor Poynting, and after him Professor Planck and Professor Ostwald, supposed this to be the case, but more recently M. Tamman has shown that such a point does not exist, and that the region of stability of the crystallized state is limited on all sides. All along the curve of transformation the two states may exist in equilibrium, but we may assert that it is impossible to realize a continuous series of intermediaries between these two states. There will always be a more or less marked discontinuity in some of the properties.

In the course of his researches M. Tamman has been led to certain very important observations, and has met with fresh allotropic modifications in nearly all substances, which singularly complicate the question. In the case of water, for instance, he finds that ordinary ice transforms itself, under a given pressure, at the temperature of -80 deg. C. into another crystalline variety which is denser than water.

The statics of solids under high pressure is as yet, therefore, hardly drafted, but it seems to promise results which will not be identical with those obtained for the statics of fluids, though it will present at least an equal interest.

Sec. 4. THE DEFORMATIONS OF SOLIDS

If the mechanical properties of the bodies intermediate between solids and liquids have only lately been the object of systematic studies, admittedly solid substances have been studied for a long time. Yet, notwithstanding the abundance of researches published on elasticity by theorists and experimenters, numerous questions with regard to them still remain in suspense.

We only propose to briefly indicate here a few problems recently examined, without going into the details of questions which belong more to the domain of mechanics than to that of pure physics.

The deformations produced in solid bodies by increasing efforts arrange themselves in two distinct periods. If the efforts are weak, the deformations produced are also very weak and disappear when the effort ceases. They are then termed elastic. If the efforts exceed a certain value, a part only of these deformations disappear, and a part are permanent.

The purity of the note emitted by a sound has been often invoked as a proof of the perfect isochronism of the oscillation, and, consequently, as a demonstration a posteriori of the correctness of the early law of Hoocke governing elastic deformations. This law has, however, during some years been frequently disputed. Certain mechanicians or physicists freely admit it to be incorrect, especially as regards extremely weak deformations. According to a theory in some favour, especially in Germany, i.e. the theory of Bach, the law which connects the elastic deformations with the efforts would be an exponential one. Recent experiments by Professors Kohlrausch and Gruncisen, executed under varied and precise conditions on brass, cast iron, slate, and wrought iron, do not appear to confirm Bach's law. Nothing, in point of fact, authorises the rejection of the law of Hoocke, which presents itself as the most natural and most simple approximation to reality.

The phenomena of permanent deformation are very complex, and it certainly seems that they cannot be explained by the older theories which insisted that the molecules only acted along the straight line which joined their centres. It becomes necessary, then, to construct more complete hypotheses, as the MM. Cosserat have done in some excellent memoirs, and we may then succeed in grouping together the facts resulting from new experiments. Among the experiments of which every theory must take account may be mentioned those by which Colonel Hartmann has placed in evidence the importance of the lines which are produced on the surface of metals when the limit of elasticity is exceeded.

It is to questions of the same order that the minute and patient researches of M. Bouasse have been directed. This physicist, as ingenious as he is profound, has pursued for several years experiments on the most delicate points relating to the theory of elasticity, and he has succeeded in defining with a precision not always attained even in the best esteemed works, the deformations to which a body must be subjected in order to obtain comparable experiments. With regard to the slight oscillations of torsion which he has specially studied, M. Bouasse arrives at the conclusion, in an acute discussion, that we hardly know anything more than was proclaimed a hundred years ago by Coulomb. We see, by this example, that admirable as is the progress accomplished in certain regions of physics, there still exist many over-neglected regions which remain in painful darkness. The skill shown by M. Bouasse authorises us to hope that, thanks to his researches, a strong light will some day illumine these unknown corners.

A particularly interesting chapter on elasticity is that relating to the study of crystals; and in the last few years it has been the object of remarkable researches on the part of M. Voigt. These researches have permitted a few controversial questions between theorists and experimenters to be solved: in particular, M. Voigt has verified the consequences of the calculations, taking care not to make, like Cauchy and Poisson, the hypothesis of central forces a mere function of distance, and has recognized a potential which depends on the relative orientation of the molecules. These considerations also apply to quasi-isotropic bodies which are, in fact, networks of crystals.

Certain occasional deformations which are produced and disappear slowly may be considered as intermediate between elastic and permanent deformations. Of these, the thermal deformation of glass which manifests itself by the displacement of the zero of a thermometer is an example. So also the modifications which the phenomena of magnetic hysteresis or the variations of resistivity have just demonstrated.

Many theorists have taken in hand these difficult questions. M. Brillouin endeavours to interpret these various phenomena by the molecular hypothesis. The attempt may seem bold, since these phenomena are, for the most part, essentially irreversible, and seem, consequently, not adaptable to mechanics. But M. Brillouin makes a point of showing that, under certain conditions, irreversible phenomena may be created between two material points, the actions of which depend solely on their distance; and he furnishes striking instances which appear to prove that a great number of irreversible physical and chemical phenomena may be ascribed to the existence of states of unstable equilibria.

M. Duhem has approached the problem from another side, and endeavours to bring it within the range of thermodynamics. Yet ordinary thermodynamics could not account for experimentally realizable states of equilibrium in the phenomena of viscosity and friction, since this science declares them to be impossible. M. Duhem, however, arrives at the idea that the establishment of the equations of thermodynamics presupposes, among other hypotheses, one which is entirely arbitrary, namely: that when the state of the system is given, external actions capable of maintaining it in that state are determined without ambiguity, by equations termed conditions of equilibrium of the system. If we reject this hypothesis, it will then be allowable to introduce into thermodynamics laws previously excluded, and it will be possible to construct, as M. Duhem has done, a much more comprehensive theory.

The ideas of M. Duhem have been illustrated by remarkable experimental work. M. Marchis, for example, guided by these ideas, has studied the permanent modifications produced in glass by an oscillation of temperature. These modifications, which may be called phenomena of the hysteresis of dilatation, may be followed in very appreciable fashion by means of a glass thermometer. The general results are quite in accord with the previsions of M. Duhem. M. Lenoble in researches on the traction of metallic wires, and M. Chevalier in experiments on the permanent variations of the electrical resistance of wires of an alloy of platinum and silver when submitted to periodical variations of temperature, have likewise afforded verifications of the theory propounded by M. Duhem.

In this theory, the representative system is considered dependent on the temperature of one or several other variables, such as, for example, a chemical variable. A similar idea has been developed in a very fine set of memoirs on nickel steel, by M. Ch. Ed. Guillaume. The eminent physicist, who, by his earlier researches, has greatly contributed to the light thrown on the analogous question of the displacement of the zero in thermometers, concludes, from fresh researches, that the residual phenomena are due to chemical variations, and that the return to the primary chemical state causes the variation to disappear. He applies his ideas not only to the phenomena presented by irreversible steels, but also to very different facts; for example, to phosphorescence, certain particularities of which may be interpreted in an analogous manner.

Nickel steels present the most curious properties, and I have already pointed out the paramount importance of one of them, hardly capable of perceptible dilatation, for its application to metrology and chronometry.[13] Others, also discovered by M. Guillaume in the course of studies conducted with rare success and remarkable ingenuity, may render great services, because it is possible to regulate, so to speak, at will their mechanical or magnetic properties.

[Footnote 13: The metal known as "invar."—ED.]

The study of alloys in general is, moreover, one of those in which the introduction of the methods of physics has produced the greatest effects. By the microscopic examination of a polished surface or of one indented by a reagent, by the determination of the electromotive force of elements of which an alloy forms one of the poles, and by the measurement of the resistivities, the densities, and the differences of potential or contact, the most valuable indications as to their constitution are obtained. M. Le Chatelier, M. Charpy, M. Dumas, M. Osmond, in France; Sir W. Roberts Austen and Mr. Stansfield, in England, have given manifold examples of the fertility of these methods. The question, moreover, has had a new light thrown upon it by the application of the principles of thermodynamics and of the phase rule.

Alloys are generally known in the two states of solid and liquid. Fused alloys consist of one or several solutions of the component metals and of a certain number of definite combinations. Their composition may thus be very complex: but Gibbs' rule gives us at once important information on the point, since it indicates that there cannot exist, in general, more than two distinct solutions in an alloy of two metals.

Solid alloys may be classed like liquid ones. Two metals or more dissolve one into the other, and form a solid solution quite analogous to the liquid solution. But the study of these solid solutions is rendered singularly difficult by the fact that the equilibrium so rapidly reached in the case of liquids in this case takes days and, in certain cases, perhaps even centuries to become established.



CHAPTER V

SOLUTIONS AND ELECTROLYTIC DISSOCIATION

Sec. 1. SOLUTION

Vaporization and fusion are not the only means by which the physical state of a body may be changed without modifying its chemical constitution. From the most remote periods solution has also been known and studied, but only in the last twenty years have we obtained other than empirical information regarding this phenomenon.

It is natural to employ here also the methods which have allowed us to penetrate into the knowledge of other transformations. The problem of solution may be approached by way of thermodynamics and of the hypotheses of kinetics.

As long ago as 1858, Kirchhoff, by attributing to saline solutions— that is to say, to mixtures of water and a non-volatile liquid like sulphuric acid—the properties of internal energy, discovered a relation between the quantity of heat given out on the addition of a certain quantity of water to a solution and the variations to which condensation and temperature subject the vapour-tension of the solution. He calculated for this purpose the variations of energy which are produced when passing from one state to another by two different series of transformations; and, by comparing the two expressions thus obtained, he established a relation between the various elements of the phenomenon. But, for a long time afterwards, the question made little progress, because there seemed to be hardly any means of introducing into this study the second principle of thermodynamics.[14] It was the memoir of Gibbs which at last opened out this rich domain and enabled it to be rationally exploited. As early as 1886, M. Duhem showed that the theory of the thermodynamic potential furnished precise information on solutions or liquid mixtures. He thus discovered over again the famous law on the lowering of the congelation temperature of solvents which had just been established by M. Raoult after a long series of now classic researches.

[Footnote 14: The "second principle" referred to has been thus enunciated: "In every engine that produces work there is a fall of temperature, and the maximum output of a perfect engine—i.e. the ratio between the heat consumed in work and the heat supplied—depends only on the extreme temperatures between which the fluid is evolved."—Demanet, Notes de Physique Experimentale, Louvain, 1905, fasc. 2, p. 147. Clausius put it in a negative form, as thus: No engine can of itself, without the aid of external agency, transfer heat from a body at low temperature to a body at a high temperature. Cf. Ganot's Physics, 17th English edition, Sec. 508.—ED.]

In the minds of many persons, however, grave doubts persisted. Solution appeared to be an essentially irreversible phenomenon. It was therefore, in all strictness, impossible to calculate the entropy of a solution, and consequently to be certain of the value of the thermodynamic potential. The objection would be serious even to-day, and, in calculations, what is called the paradox of Gibbs would be an obstacle.

We should not hesitate, however, to apply the Phase Law to solutions, and this law already gives us the key to a certain number of facts. It puts in evidence, for example, the part played by the eutectic point— that is to say, the point at which (to keep to the simple case in which we have to do with two bodies only, the solvent and the solute) the solution is in equilibrium at once with the two possible solids, the dissolved body and the solvent solidified. The knowledge of this point explains the properties of refrigerating mixtures, and it is also one of the most useful for the theory of alloys. The scruples of physicists ought to have been removed on the memorable occasion when Professor Van t'Hoff demonstrated that solution can operate reversibly by reason of the phenomena of osmosis. But the experiment can only succeed in very rare cases; and, on the other hand, Professor Van t'Hoff was naturally led to another very bold conception. He regarded the molecule of the dissolved body as a gaseous one, and assimilated solution, not as had hitherto been the rule, to fusion, but to a kind of vaporization. Naturally his ideas were not immediately accepted by the scholars most closely identified with the classic tradition. It may perhaps not be without use to examine here the principles of Professor Van t'Hoff's theory.

Sec. 2. OSMOSIS

Osmosis, or diffusion through a septum, is a phenomenon which has been known for some time. The discovery of it is attributed to the Abbe Nollet, who is supposed to have observed it in 1748, during some "researches on liquids in ebullition." A classic experiment by Dutrochet, effected about 1830, makes this phenomenon clear. Into pure water is plunged the lower part of a vertical tube containing pure alcohol, open at the top and closed at the bottom by a membrane, such as a pig's bladder, without any visible perforation. In a very short time it will be found, by means of an areometer for instance, that the water outside contains alcohol, while the alcohol of the tube, pure at first, is now diluted. Two currents have therefore passed through the membrane, one of water from the outside to the inside, and one of alcohol in the converse direction. It is also noted that a difference in the levels has occurred, and that the liquid in the tube now rises to a considerable height. It must therefore be admitted that the flow of the water has been more rapid than that of the alcohol. At the commencement, the water must have penetrated into the tube much more rapidly than the alcohol left it. Hence the difference in the levels, and, consequently, a difference of pressure on the two faces of the membrane. This difference goes on increasing, reaches a maximum, then diminishes, and vanishes when the diffusion is complete, final equilibrium being then attained.

The phenomenon is evidently connected with diffusion. If water is very carefully poured on to alcohol, the two layers, separate at first, mingle by degrees till a homogeneous substance is obtained. The bladder seems not to have prevented this diffusion from taking place, but it seems to have shown itself more permeable to water than to alcohol. May it not therefore be supposed that there must exist dividing walls in which this difference of permeability becomes greater and greater, which would be permeable to the solvent and absolutely impermeable to the solute? If this be so, the phenomena of these semi-permeable walls, as they are termed, can be observed in particularly simple conditions.

The answer to this question has been furnished by biologists, at which we cannot be surprised. The phenomena of osmosis are naturally of the first importance in the action of organisms, and for a long time have attracted the attention of naturalists. De Vries imagined that the contractions noticed in the protoplasm of cells placed in saline solutions were due to a phenomenon of osmosis, and, upon examining more closely certain peculiarities of cell life, various scholars have demonstrated that living cells are enclosed in membranes permeable to certain substances and entirely impermeable to others. It was interesting to try to reproduce artificially semi-permeable walls analogous to those thus met with in nature;[15] and Traube and Pfeffer seem to have succeeded in one particular case. Traube has pointed out that the very delicate membrane of ferrocyanide of potassium which is obtained with some difficulty by exposing it to the reaction of sulphate of copper, is permeable to water, but will not permit the passage of the majority of salts. Pfeffer, by producing these walls in the interstices of a porous porcelain, has succeeded in giving them sufficient rigidity to allow measurements to be made. It must be allowed that, unfortunately, no physicist or chemist has been as lucky as these two botanists; and the attempts to reproduce semi-permeable walls completely answering to the definition, have never given but mediocre results. If, however, the experimental difficulty has not been overcome in an entirely satisfactory manner, it at least appears very probable that such walls may nevertheless exist.[16]

[Footnote 15: See next note.—ED.]

[Footnote 16: M. Stephane Leduc, Professor of Biology of Nantes, has made many experiments in this connection, and the artificial cells exhibited by him to the Association francaise pour l'avancement des Sciences, at their meeting at Grenoble in 1904 and reproduced in their "Actes," are particularly noteworthy.—ED.]

Nevertheless, in the case of gases, there exists an excellent example of a semi-permeable wall, and a partition of platinum brought to a higher than red heat is, as shown by M. Villard in some ingenious experiments, completely impermeable to air, and very permeable, on the contrary, to hydrogen. It can also be experimentally demonstrated that on taking two recipients separated by such a partition, and both containing nitrogen mixed with varying proportions of hydrogen, the last-named gas will pass through the partition in such a way that the concentration—that is to say, the mass of gas per unit of volume— will become the same on both sides. Only then will equilibrium be established; and, at that moment, an excess of pressure will naturally be produced in that recipient which, at the commencement, contained the gas with the smallest quantity of hydrogen.

This experiment enables us to anticipate what will happen in a liquid medium with semi-permeable partitions. Between two recipients, one containing pure water, the other, say, water with sugar in solution, separated by one of these partitions, there will be produced merely a movement of the pure towards the sugared water, and following this, an increase of pressure on the side of the last. But this increase will not be without limits. At a certain moment the pressure will cease to increase and will remain at a fixed value which now has a given direction. This is the osmotic pressure.

Pfeffer demonstrated that, for the same substance, the osmotic pressure is proportional to the concentration, and consequently in inverse ratio to the volume occupied by a similar mass of the solute. He gave figures from which it was easy, as Professor Van t'Hoff found, to draw the conclusion that, in a constant volume, the osmotic pressure is proportional to the absolute temperature. De Vries, moreover, by his remarks on living cells, extended the results which Pfeffer had applied to one case only—that is, to the one that he had been able to examine experimentally.

Such are the essential facts of osmosis. We may seek to interpret them and to thoroughly examine the mechanism of the phenomenon; but it must be acknowledged that as regards this point, physicists are not entirely in accord. In the opinion of Professor Nernst, the permeability of semi-permeable membranes is simply due to differences of solubility in one of the substances of the membrane itself. Other physicists think it attributable, either to the difference in the dimensions of the molecules, of which some might pass through the pores of the membrane and others be stopped by their relative size, or to these molecules' greater or less mobility. For others, again, it is the capillary phenomena which here act a preponderating part.

This last idea is already an old one: Jager, More, and Professor Traube have all endeavoured to show that the direction and speed of osmosis are determined by differences in the surface-tensions; and recent experiments, especially those of Batelli, seem to prove that osmosis establishes itself in the way which best equalizes the surface-tensions of the liquids on both sides of the partition. Solutions possessing the same surface-tension, though not in molecular equilibrium, would thus be always in osmotic equilibrium. We must not conceal from ourselves that this result would be in contradiction with the kinetic theory.

Sec. 3. APPLICATION TO THE THEORY OF SOLUTION

If there really exist partitions permeable to one body and impermeable to another, it may be imagined that the homogeneous mixture of these two bodies might be effected in the converse way. It can be easily conceived, in fact, that by the aid of osmotic pressure it would be possible, for example, to dilute or concentrate a solution by driving through the partition in one direction or another a certain quantity of the solvent by means of a pressure kept equal to the osmotic pressure. This is the important fact which Professor Van t' Hoff perceived. The existence of such a wall in all possible cases evidently remains only a very legitimate hypothesis,—a fact which ought not to be concealed.

Relying solely on this postulate, Professor Van t' Hoff easily established, by the most correct method, certain properties of the solutions of gases in a volatile liquid, or of non-volatile bodies in a volatile liquid. To state precisely the other relations, we must admit, in addition, the experimental laws discovered by Pfeffer. But without any hypothesis it becomes possible to demonstrate the laws of Raoult on the lowering of the vapour-tension and of the freezing point of solutions, and also the ratio which connects the heat of fusion with this decrease.

These considerable results can evidently be invoked as a posteriori proofs of the exactitude of the experimental laws of osmosis. They are not, however, the only ones that Professor Van t' Hoff has obtained by the same method. This illustrious scholar was thus able to find anew Guldberg and Waage's law on chemical equilibrium at a constant temperature, and to show how the position of the equilibrium changes when the temperature happens to change.

If now we state, in conformity with the laws of Pfeffer, that the product of the osmotic pressure by the volume of the solution is equal to the absolute temperature multiplied by a coefficient, and then look for the numerical figure of this latter in a solution of sugar, for instance, we find that this value is the same as that of the analogous coefficient of the characteristic equation of a perfect gas. There is in this a coincidence which has also been utilized in the preceding thermodynamic calculations. It may be purely fortuitous, but we can hardly refrain from finding in it a physical meaning.

Professor Van t'Hoff has considered this coincidence a demonstration that there exists a strong analogy between a body in solution and a gas; as a matter of fact, it may seem that, in a solution, the distance between the molecules becomes comparable to the molecular distances met with in gases, and that the molecule acquires the same degree of liberty and the same simplicity in both phenomena. In that case it seems probable that solutions will be subject to laws independent of the chemical nature of the dissolved molecule and comparable to the laws governing gases, while if we adopt the kinetic image for the gas, we shall be led to represent to ourselves in a similar way the phenomena which manifest themselves in a solution. Osmotic pressure will then appear to be due to the shock of the dissolved molecules against the membrane. It will come from one side of this partition to superpose itself on the hydrostatic pressure, which latter must have the same value on both sides.

The analogy with a perfect gas naturally becomes much greater as the solution becomes more diluted. It then imitates gas in some other properties; the internal work of the variation of volume is nil, and the specific heat is only a function of the temperature. A solution which is diluted by a reversible method is cooled like a gas which expands adiabatically.[17]

[Footnote 17: That is, without receiving or emitting any heat.—ED.]

It must, however, be acknowledged that, in other points, the analogy is much less perfect. The opinion which sees in solution a phenomenon resembling fusion, and which has left an indelible trace in everyday language (we shall always say: to melt sugar in water) is certainly not without foundation. Certain of the reasons which might be invoked to uphold this opinion are too evident to be repeated here, though others more recondite might be quoted. The fact that the internal energy generally becomes independent of the concentration when the dilution reaches even a moderately high value is rather in favour of the hypothesis of fusion.

We must not forget, however, the continuity of the liquid and gaseous states; and we may consider it in an absolute way a question devoid of sense to ask whether in a solution the solute is in the liquid or the gaseous state. It is in the fluid state, and perhaps in conditions opposed to those of a body in the state of a perfect gas. It is known, of course, that in this case the manometrical pressure must be regarded as very great in relation to the internal pressure which, in the characteristic equation, is added to the other. May it not seem possible that in the solution it is, on the contrary, the internal pressure which is dominant, the manometric pressure becoming of no account? The coincidence of the formulas would thus be verified, for all the characteristic equations are symmetrical with regard to these two pressures. From this point of view the osmotic pressure would be considered as the result of an attraction between the solvent and the solute; and it would represent the difference between the internal pressures of the solution and of the pure solvent. These hypotheses are highly interesting, and very suggestive; but from the way in which the facts have been set forth, it will appear, no doubt, that there is no obligation to admit them in order to believe in the legitimacy of the application of thermodynamics to the phenomena of solution.

Sec. 4. ELECTROLYTIC DISSOCIATION

From the outset Professor Van t' Hoff was brought to acknowledge that a great number of solutions formed very notable exceptions which were very irregular in appearance. The analogy with gases did not seem to be maintained, for the osmotic pressure had a very different value from that indicated by the theory. Everything, however, came right if one multiplied by a factor, determined according to each case, but greater than unity, the constant of the characteristic formula. Similar divergences were manifested in the delays observed in congelation, and disappeared when subjected to an analogous correction.

Thus the freezing-point of a normal solution, containing a molecule gramme (that is, the number of grammes equal to the figure representing the molecular mass) of alcohol or sugar in water, falls 1.85 deg. C. If the laws of solution were identically the same for a solution of sea-salt, the same depression should be noticed in a saline solution also containing 1 molecule per litre. In fact, the fall reaches 3.26 deg., and the solution behaves as if it contained, not 1, but 1.75 normal molecules per litre. The consideration of the osmotic pressures would lead to similar observations, but we know that the experiment would be more difficult and less precise.

We may wonder whether anything really analogous to this can be met with in the case of a gas, and we are thus led to consider the phenomena of dissociation.[18] If we heat a body which, in a gaseous state, is capable of dissociation—hydriodic acid, for example—at a given temperature, an equilibrium is established between three gaseous bodies, the acid, the iodine, and the hydrogen. The total mass will follow with fair closeness Mariotte's law, but the characteristic constant will no longer be the same as in the case of a non-dissociated gas. We here no longer have to do with a single molecule, since each molecule is in part dissociated.

[Footnote 18: Dissociation must be distinguished from decomposition, which is what occurs when the whole of a particle (compound, molecule, atom, etc.) breaks up into its component parts. In dissociation the breaking up is only partial, and the resultant consists of a mixture of decomposed and undecomposed parts. See Ganot's Physics, 17th English edition, Sec. 395, for examples.—ED.]

The comparison of the two cases leads to the employment of a new image for representing the phenomenon which has been produced throughout the saline solution. We have introduced a single molecule of salt, and everything occurs as if there were 1.75 molecules. May it not really be said that the number is 1.75, because the sea-salt is partly dissociated, and a molecule has become transformed into 0.75 molecule of sodium, 0.75 of chlorium, and 0.25 of salt?

This is a way of speaking which seems, at first sight, strangely contradicted by experiment. Professor Van t' Hoff, like other chemists, would certainly have rejected—in fact, he did so at first— such a conception, if, about the same time, an illustrious Swedish scholar, M. Arrhenius, had not been brought to the same idea by another road, and, had not by stating it precisely and modifying it, presented it in an acceptable form.

A brief examination will easily show that all the substances which are exceptions to the laws of Van t'Hoff are precisely those which are capable of conducting electricity when undergoing decomposition—that is to say, are electrolytes. The coincidence is absolute, and cannot be simply due to chance.

Now, the phenomena of electrolysis have, for a long time, forced upon us an almost necessary image. The saline molecule is always decomposed, as we know, in the primary phenomenon of electrolysis into two elements which Faraday termed ions. Secondary reactions, no doubt, often come to complicate the question, but these are chemical reactions belonging to the general order of things, and have nothing to do with the electric action working on the solution. The simple phenomenon is always the same—decomposition into two ions, followed by the appearance of one of these ions at the positive and of the other at the negative electrode. But as the very slightest expenditure of energy is sufficient to produce the commencement of electrolysis, it is necessary to suppose that these two ions are not united by any force. Thus the two ions are, in a way, dissociated. Clausius, who was the first to represent the phenomena by this symbol, supposed, in order not to shock the feelings of chemists too much, that this dissociation only affected an infinitesimal fraction of the total number of the molecules of the salt, and thereby escaped all check.

This concession was unfortunate, and the hypothesis thus lost the greater part of its usefulness. M. Arrhenius was bolder, and frankly recognized that dissociation occurs at once in the case of a great number of molecules, and tends to increase more and more as the solution becomes more dilute. It follows the comparison with a gas which, while partially dissociated in an enclosed space, becomes wholly so in an infinite one.

M. Arrhenius was led to adopt this hypothesis by the examination of experimental results relating to the conductivity of electrolytes. In order to interpret certain facts, it has to be recognized that a part only of the molecules in a saline solution can be considered as conductors of electricity, and that by adding water the number of molecular conductors is increased. This increase, too, though rapid at first, soon becomes slower, and approaches a certain limit which an infinite dilution would enable it to attain. If the conducting molecules are the dissociated molecules, then the dissociation (so long as it is a question of strong acids and salts) tends to become complete in the case of an unlimited dilution.

The opposition of a large number of chemists and physicists to the ideas of M. Arrhenius was at first very fierce. It must be noted with regret that, in France particularly, recourse was had to an arm which scholars often wield rather clumsily. They joked about these free ions in solution, and they asked to see this chlorine and this sodium which swam about the water in a state of liberty. But in science, as elsewhere, irony is not argument, and it soon had to be acknowledged that the hypothesis of M. Arrhenius showed itself singularly fertile and had to be regarded, at all events, as a very expressive image, if not, indeed, entirely in conformity with reality.

It would certainly be contrary to all experience, and even to common sense itself, to suppose that in dissolved chloride of sodium there is really free sodium, if we suppose these atoms of sodium to be absolutely identical with ordinary atoms. But there is a great difference. In the one case the atoms are electrified, and carry a relatively considerable positive charge, inseparable from their state as ions, while in the other they are in the neutral state. We may suppose that the presence of this charge brings about modifications as extensive as one pleases in the chemical properties of the atom. Thus the hypothesis will be removed from all discussion of a chemical order, since it will have been made plastic enough beforehand to adapt itself to all the known facts; and if we object that sodium cannot subsist in water because it instantaneously decomposes the latter, the answer is simply that the sodium ion does not decompose water as does ordinary sodium.

Still, other objections might be raised which could not be so easily refuted. One, to which chemists not unreasonably attached great importance, was this:—If a certain quantity of chloride of sodium is dissociated into chlorine and sodium, it should be possible, by diffusion, for example, which brings out plainly the phenomena of dissociation in gases, to extract from the solution a part either of the chlorine or of the sodium, while the corresponding part of the other compound would remain. This result would be in flagrant contradiction with the fact that, everywhere and always, a solution of salt contains strictly the same proportions of its component elements.

M. Arrhenius answers to this that the electrical forces in ordinary conditions prevent separation by diffusion or by any other process. Professor Nernst goes further, and has shown that the concentration currents which are produced when two electrodes of the same substance are plunged into two unequally concentrated solutions may be interpreted by the hypothesis that, in these particular conditions, the diffusion does bring about a separation of the ions. Thus the argument is turned round, and the proof supposed to be given of the incorrectness of the theory becomes a further reason in its favour.

It is possible, no doubt, to adduce a few other experiments which are not very favourable to M. Arrhenius's point of view, but they are isolated cases; and, on the whole, his theory has enabled many isolated facts, till then scattered, to be co-ordinated, and has allowed very varied phenomena to be linked together. It has also suggested—and, moreover, still daily suggests—researches of the highest order.

In the first place, the theory of Arrhenius explains electrolysis very simply. The ions which, so to speak, wander about haphazard, and are uniformly distributed throughout the liquid, steer a regular course as soon as we dip in the trough containing the electrolyte the two electrodes connected with the poles of the dynamo or generator of electricity. Then the charged positive ions travel in the direction of the electromotive force and the negative ions in the opposite direction. On reaching the electrodes they yield up to them the charges they carry, and thus pass from the state of ion into that of ordinary atom. Moreover, for the solution to remain in equilibrium, the vanished ions must be immediately replaced by others, and thus the state of ionisation of the electrolyte remains constant and its conductivity persists.

All the peculiarities of electrolysis are capable of interpretation: the phenomena of the transport of ions, the fine experiments of M. Bouty, those of Professor Kohlrausch and of Professor Ostwald on various points in electrolytic conduction, all support the theory. The verifications of it can even be quantitative, and we can foresee numerical relations between conductivity and other phenomena. The measurement of the conductivity permits the number of molecules dissociated in a given solution to be calculated, and the number is thus found to be precisely the same as that arrived at if it is wished to remove the disagreement between reality and the anticipations which result from the theory of Professor Van t' Hoff. The laws of cryoscopy, of tonometry, and of osmosis thus again become strict, and no exception to them remains.

If the dissociation of salts is a reality and is complete in a dilute solution, any of the properties of a saline solution whatever should be represented numerically as the sum of three values, of which one concerns the positive ion, a second the negative ion, and the third the solvent. The properties of the solutions would then be what are called additive properties. Numerous verifications may be attempted by very different roads. They generally succeed very well; and whether we measure the electric conductivity, the density, the specific heats, the index of refraction, the power of rotatory polarization, the colour, or the absorption spectrum, the additive property will everywhere be found in the solution.

The hypothesis, so contested at the outset by the chemists, is, moreover, assuring its triumph by important conquests in the domain of chemistry itself. It permits us to give a vivid explanation of chemical reaction, and for the old motto of the chemists, "Corpora non agunt, nisi soluta," it substitutes a modern one, "It is especially the ions which react." Thus, for example, all salts of iron, which contain iron in the state of ions, give similar reactions; but salts such as ferrocyanide of potassium, in which iron does not play the part of an ion, never give the characteristic reactions of iron.

Professor Ostwald and his pupils have drawn from the hypothesis of Arrhenius manifold consequences which have been the cause of considerable progress in physical chemistry. Professor Ostwald has shown, in particular, how this hypothesis permits the quantitative calculation of the conditions of equilibrium of electrolytes and solutions, and especially of the phenomena of neutralization. If a dissolved salt is partly dissociated into ions, this solution must be limited by an equilibrium between the non-dissociated molecule and the two ions resulting from the dissociation; and, assimilating the phenomenon to the case of gases, we may take for its study the laws of Gibbs and of Guldberg and Waage. The results are generally very satisfactory, and new researches daily furnish new checks.

Professor Nernst, who before gave, as has been said, a remarkable interpretation of the diffusion of electrolytes, has, in the direction pointed out by M. Arrhenius, developed a theory of the entire phenomena of electrolysis, which, in particular, furnishes a striking explanation of the mechanism of the production of electromotive force in galvanic batteries.

Extending the analogy, already so happily invoked, between the phenomena met with in solutions and those produced in gases, Professor Nernst supposes that metals tend, as it were, to vaporize when in presence of a liquid. A piece of zinc introduced, for example, into pure water gives birth to a few metallic ions. These ions become positively charged, while the metal naturally takes an equal charge, but of contrary sign. Thus the solution and the metal are both electrified; but this sort of vaporization is hindered by electrostatic attraction, and as the charges borne by the ions are considerable, an equilibrium will be established, although the number of ions which enter the solution will be very small.

If the liquid, instead of being a solvent like pure water, contains an electrolyte, it already contains metallic ions, the osmotic pressure of which will be opposite to that of the solution. Three cases may then present themselves—either there will be equilibrium, or the electrostatic attraction will oppose itself to the pressure of solution and the metal will be negatively charged, or, finally, the attraction will act in the same direction as the pressure, and the metal will become positively and the solution negatively charged. Developing this idea, Professor Nernst calculates, by means of the action of the osmotic pressures, the variations of energy brought into play and the value of the differences of potential by the contact of the electrodes and electrolytes. He deduces this from the electromotive force of a single battery cell which becomes thus connected with the values of the osmotic pressures, or, if you will, thanks to the relation discovered by Van t' Hoff, with the concentrations. Some particularly interesting electrical phenomena thus become connected with an already very important group, and a new bridge is built which unites two regions long considered foreign to each other.

The recent discoveries on the phenomena produced in gases when rendered conductors of electricity almost force upon us, as we shall see, the idea that there exist in these gases electrified centres moving through the field, and this idea gives still greater probability to the analogous theory explaining the mechanism of the conductivity of liquids. It will also be useful, in order to avoid confusion, to restate with precision this notion of electrolytic ions, and to ascertain their magnitude, charge, and velocity.

The two classic laws of Faraday will supply us with important information. The first indicates that the quantity of electricity passing through the liquid is proportional to the quantity of matter deposited on the electrodes. This leads us at once to the consideration that, in any given solution, all the ions possess individual charges equal in absolute value.

The second law may be stated in these terms: an atom-gramme of metal carries with it into electrolysis a quantity of electricity proportionate to its valency.[19]

[Footnote 19: The valency or atomicity of an element may be defined as the power it possesses of entering into compounds in a certain fixed proportion. As hydrogen is generally taken as the standard, in practice the valency of an atom is the number of hydrogen atoms it will combine with or replace. Thus chlorine and the rest of the halogens, the atoms of which combine with one atom of hydrogen, are called univalent, oxygen a bivalent element, and so on.—ED.]

Numerous experiments have made known the total mass of hydrogen capable of carrying one coulomb, and it will therefore be possible to estimate the charge of an ion of hydrogen if the number of atoms of hydrogen in a given mass be known. This last figure is already furnished by considerations derived from the kinetic theory, and agrees with the one which can be deduced from the study of various phenomena. The result is that an ion of hydrogen having a mass of 1.3 x 10^{-20} grammes bears a charge of 1.3 X 10^{-20} electromagnetic units; and the second law will immediately enable the charge of any other ion to be similarly estimated.

The measurements of conductivity, joined to certain considerations relating to the differences of concentration which appear round the electrode in electrolysis, allow the speed of the ions to be calculated. Thus, in a liquid containing 1/10th of a hydrogen-ion per litre, the absolute speed of an ion would be 3/10ths of a millimetre per second in a field where the fall of potential would be 1 volt per centimetre. Sir Oliver Lodge, who has made direct experiments to measure this speed, has obtained a figure very approximate to this. This value is very small compared to that which we shall meet with in gases.

Another consequence of the laws of Faraday, to which, as early as 1881, Helmholtz drew attention, may be considered as the starting-point of certain new doctrines we shall come across later.

Helmholtz says: "If we accept the hypothesis that simple bodies are composed of atoms, we are obliged to admit that, in the same way, electricity, whether positive or negative, is composed of elementary parts which behave like atoms of electricity."

The second law seems, in fact, analogous to the law of multiple proportions in chemistry, and it shows us that the quantities of electricity carried vary from the simple to the double or treble, according as it is a question of a uni-, bi-, or trivalent metal; and as the chemical law leads up to the conception of the material atom, so does the electrolytic law suggest the idea of an electric atom.



CHAPTER VI

THE ETHER

Sec. 1. THE LUMINIFEROUS ETHER

It is in the works of Descartes that we find the first idea of attributing those physical phenomena which the properties of matter fail to explain to some subtle matter which is the receptacle of the energy of the universe.

In our times this idea has had extraordinary luck. After having been eclipsed for two hundred years by the success of the immortal synthesis of Newton, it gained an entirely new splendour with Fresnel and his followers. Thanks to their admirable discoveries, the first stage seemed accomplished, the laws of optics were represented by a single hypothesis, marvellously fitted to allow us to anticipate unknown phenomena, and all these anticipations were subsequently fully verified by experiment. But the researches of Faraday, Maxwell, and Hertz authorized still greater ambitions; and it really seemed that this medium, to which it was agreed to give the ancient name of ether, and which had already explained light and radiant heat, would also be sufficient to explain electricity. Thus the hope began to take form that we might succeed in demonstrating the unity of all physical forces. It was thought that the knowledge of the laws relating to the inmost movements of this ether might give us the key to all phenomena, and might make us acquainted with the method in which energy is stored up, transmitted, and parcelled out in its external manifestations.

We cannot study here all the problems which are connected with the physics of the ether. To do this a complete treatise on optics would have to be written and a very lengthy one on electricity. I shall simply endeavour to show rapidly how in the last few years the ideas relative to the constitution of this ether have evolved, and we shall see if it be possible without self-delusion to imagine that a single medium can really allow us to group all the known facts in one comprehensive arrangement.

As constructed by Fresnel, the hypothesis of the luminous ether, which had so great a struggle at the outset to overcome the stubborn resistance of the partisans of the then classic theory of emission, seemed, on the contrary, to possess in the sequel an unshakable strength. Lame, though a prudent mathematician, wrote: "The existence of the ethereal fluid is incontestably demonstrated by the propagation of light through the planetary spaces, and by the explanation, so simple and so complete, of the phenomena of diffraction in the wave theory of light"; and he adds: "The laws of double refraction prove with no less certainty that the ether exists in all diaphanous media." Thus the ether was no longer an hypothesis, but in some sort a tangible reality. But the ethereal fluid of which the existence was thus proclaimed has some singular properties.

Were it only a question of explaining rectilinear propagation, reflexion, refraction, diffraction, and interferences notwithstanding grave difficulties at the outset and the objections formulated by Laplace and Poisson (some of which, though treated somewhat lightly at the present day, have not lost all value), we should be under no obligation to make any hypothesis other than that of the undulations of an elastic medium, without deciding in advance anything as to the nature and direction of the vibrations.

This medium would, naturally—since it exists in what we call the void—be considered as imponderable. It may be compared to a fluid of negligible mass—since it offers no appreciable resistance to the motion of the planets—but is endowed with an enormous elasticity, because the velocity of the propagation of light is considerable. It must be capable of penetrating into all transparent bodies, and of retaining there, so to speak, a constant elasticity, but must there become condensed, since the speed of propagation in these bodies is less than in a vacuum. Such properties belong to no material gas, even the most rarefied, but they admit of no essential contradiction, and that is the important point.[20]

[Footnote 20: Since this was written, however, men of science have become less unanimous than they formerly were on this point. The veteran chemist Professor Mendeleeff has given reasons for thinking that the ether is an inert gas with an atomic weight a million times less than that of hydrogen, and a velocity of 2250 kilometres per second (Principles of Chemistry, Eng. ed., 1905, vol. ii. p. 526). On the other hand, the well-known physicist Dr A.H. Bucherer, speaking at the Naturforscherversammlung, held at Stuttgart in 1906, declared his disbelief in the existence of the ether, which he thought could not be reconciled at once with the Maxwellian theory and the known facts.—ED.]

It was the study of the phenomena of polarization which led Fresnel to his bold conception of transverse vibrations, and subsequently induced him to penetrate further into the constitution of the ether. We know the experiment of Arago on the noninterference of polarized rays in rectangular planes. While two systems of waves, proceeding from the same source of natural light and propagating themselves in nearly parallel directions, increase or become destroyed according to whether the nature of the superposed waves are of the same or of contrary signs, the waves of the rays polarized in perpendicular planes, on the other hand, can never interfere with each other. Whatever the difference of their course, the intensity of the light is always the sum of the intensity of the two rays.

Fresnel perceived that this experiment absolutely compels us to reject the hypothesis of longitudinal vibrations acting along the line of propagation in the direction of the rays. To explain it, it must of necessity be admitted, on the contrary, that the vibrations are transverse and perpendicular to the ray. Verdet could say, in all truth, "It is not possible to deny the transverse direction of luminous vibrations, without at the same time denying that light consists of an undulatory movement."

Such vibrations do not and cannot exist in any medium resembling a fluid. The characteristic of a fluid is that its different parts can displace themselves with regard to one another without any reaction appearing so long as a variation of volume is not produced. There certainly may exist, as we have seen, certain traces of rigidity in a liquid, but we cannot conceive such a thing in a body infinitely more subtle than rarefied gas. Among material bodies, a solid alone really possesses the rigidity sufficient for the production within it of transverse vibrations and for their maintenance during their propagation.

Since we have to attribute such a property to the ether, we may add that on this point it resembles a solid, and Lord Kelvin has shown that this solid, would be much more rigid than steel. This conclusion produces great surprise in all who hear it for the first time, and it is not rare to hear it appealed to as an argument against the actual existence of the ether. It does not seem, however, that such an argument can be decisive. There is no reason for supposing that the ether ought to be a sort of extension of the bodies we are accustomed to handle. Its properties may astonish our ordinary way of thinking, but this rather unscientific astonishment is not a reason for doubting its existence. Real difficulties would appear only if we were led to attribute to the ether, not singular properties which are seldom found united in the same substance, but properties logically contradictory. In short, however odd such a medium may appear to us, it cannot be said that there is any absolute incompatibility between its attributes.

It would even be possible, if we wished, to suggest images capable of representing these contrary appearances. Various authors have done so. Thus, M. Boussinesq assumes that the ether behaves like a very rarefied gas in respect of the celestial bodies, because these last move, while bathed in it, in all directions and relatively slowly, while they permit it to retain, so to speak, its perfect homogeneity. On the other hand, its own undulations are so rapid that so far as they are concerned the conditions become very different, and its fluidity has, one might say, no longer the time to come in. Hence its rigidity alone appears.

Another consequence, very important in principle, of the fact that vibrations of light are transverse, has been well put in evidence by Fresnel. He showed how we have, in order to understand the action which excites without condensation the sliding of successive layers of the ether during the propagation of a vibration, to consider the vibrating medium as being composed of molecules separated by finite distances. Certain authors, it is true, have proposed theories in which the action at a distance of these molecules are replaced by actions of contact between parallelepipeds sliding over one another; but, at bottom, these two points of view both lead us to conceive the ether as a discontinuous medium, like matter itself. The ideas gathered from the most recent experiments also bring us to the same conclusion.

Sec. 2. RADIATIONS

In the ether thus constituted there are therefore propagated transverse vibrations, regarding which all experiments in optics furnish very precise information. The amplitude of these vibrations is exceedingly small, even in relation to the wave-length, small as these last are. If, in fact, the amplitude of the vibrations acquired a noticeable value in comparison with the wave-length, the speed of propagation should increase with the amplitude. Yet, in spite of some curious experiments which seem to establish that the speed of light does alter a little with its intensity, we have reason to believe that, as regards light, the amplitude of the oscillations in relation to the wave-length is incomparably less than in the case of sound.

It has become the custom to characterise each vibration by the path which the vibratory movement traverses during the space of a vibration—by the length of wave, in a word—rather than by the duration of the vibration itself. To measure wave-lengths, the methods must be employed to which I have already alluded on the subject of measurements of length. Professor Michelson, on the one hand, and MM. Perot and Fabry, on the other, have devised exceedingly ingenious processes, which have led to results of really unhoped-for precision. The very exact knowledge also of the speed of the propagation of light allows the duration of a vibration to be calculated when once the wave-length is known. It is thus found that, in the case of visible light, the number of the vibrations from the end of the violet to the infra-red varies from four hundred to two hundred billions per second. This gamut is not, however, the only one the ether can give. For a long time we have known ultra-violet radiations still more rapid, and, on the other hand, infra-red ones more slow, while in the last few years the field of known radiations has been singularly extended in both directions.

It is to M. Rubens and his fellow-workers that are due the most brilliant conquests in the matter of great wave-lengths. He had remarked that, in their study, the difficulty of research proceeds from the fact that the extreme waves of the infra-red spectrum only contain a small part of the total energy emitted by an incandescent body; so that if, for the purpose of study, they are further dispersed by a prism or a grating, the intensity at any one point becomes so slight as to be no longer observable. His original idea was to obtain, without prism or grating, a homogeneous pencil of great wave-length sufficiently intense to be examined. For this purpose the radiant source used was a strip of platinum covered with fluorine or powdered quartz, which emits numerous radiations close to two bands of linear absorption in the absorption spectra of fluorine and quartz, one of which is situated in the infra-red. The radiations thus emitted are several times reflected on fluorine or on quartz, as the case may be; and as, in proximity to the bands, the absorption is of the order of that of metallic bodies for luminous rays, we no longer meet in the pencil several times reflected or in the rays remaining after this kind of filtration, with any but radiations of great wave-length. Thus, for instance, in the case of the quartz, in the neighbourhood of a radiation corresponding to a wave-length of 8.5 microns, the absorption is thirty times greater in the region of the band than in the neighbouring region, and consequently, after three reflexions, while the corresponding radiations will not have been weakened, the neighbouring waves will be so, on the contrary, in the proportion of 1 to 27,000.

With mirrors of rock salt and of sylvine[21] there have been obtained, by taking an incandescent gas light (Auer) as source, radiations extending as far as 70 microns; and these last are the greatest wave-lengths observed in optical phenomena. These radiations are largely absorbed by the vapour of water, and it is no doubt owing to this absorption that they are not found in the solar spectrum. On the other hand, they easily pass through gutta-percha, india-rubber, and insulating substances in general.

[Footnote 21: A natural chlorate of potassium, generally of volcanic origin.—ED.]

At the opposite end of the spectrum the knowledge of the ultra-violet regions has been greatly extended by the researches of Lenard. These extremely rapid radiations have been shown by that eminent physicist to occur in the light of the electric sparks which flash between two metal points, and which are produced by a large induction coil with condenser and a Wehnelt break. Professor Schumann has succeeded in photographing them by depositing bromide of silver directly on glass plates without fixing it with gelatine; and he has, by the same process, photographed in the spectrum of hydrogen a ray with a wave-length of only 0.1 micron.

The spectroscope was formed entirely of fluor-spar, and a vacuum had been created in it, for these radiations are extremely absorbable by the air.

Notwithstanding the extreme smallness of the luminous wave-lengths, it has been possible, after numerous fruitless trials, to obtain stationary waves analogous to those which, in the case of sound, are produced in organ pipes. The marvellous application M. Lippmann has made of these waves to completely solve the problem of photography in colours is well known. This discovery, so important in itself and so instructive, since it shows us how the most delicate anticipations of theory may be verified in all their consequences, and lead the physicist to the solution of the problems occurring in practice, has justly become popular, and there is, therefore, no need to describe it here in detail.

Professor Wiener obtained stationary waves some little while before M. Lippmann's discovery, in a layer of a sensitive substance having a grain sufficiently small in relation to the length of wave. His aim was to solve a question of great importance to a complete knowledge of the ether. Fresnel founded his theory of double refraction and reflexion by transparent surfaces, on the hypothesis that the vibration of a ray of polarized light is perpendicular to the plane of polarization. But Neumann has proposed, on the contrary, a theory in which he recognizes that the luminous vibration is in this very plane. He rather supposes, in opposition to Fresnel's idea, that the density of the ether remains the same in all media, while its coefficient of elasticity is variable.

Very remarkable experiments on dispersion by M. Carvallo prove indeed that the idea of Fresnel was, if not necessary for us to adopt, at least the more probable of the two; but apart from this indication, and contrary to the hypothesis of Neumann, the two theories, from the point of view of the explanation of all known facts, really appear to be equivalent. Are we then in presence of two mechanical explanations, different indeed, but nevertheless both adaptable to all the facts, and between which it will always be impossible to make a choice? Or, on the contrary, shall we succeed in realising an experimentum crucis, an experiment at the point where the two theories cross, which will definitely settle the question?

Professor Wiener thought he could draw from his experiment a firm conclusion on the point in dispute. He produced stationary waves with light polarized at an angle of 45 deg.,[22] and established that, when light is polarized in the plane of incidence, the fringes persist; but that, on the other hand, they disappear when the light is polarized perpendicularly to this plane. If it be admitted that a photographic impression results from the active force of the vibratory movement of the ether, the question is, in fact, completely elucidated, and the discrepancy is abolished in Fresnel's favour.

[Footnote 22: That is to say, he reflected the beam of polarized light by a mirror placed at that angle. See Turpain, Lecons elementaires de Physique, t. ii. p. 311, for details of the experiment.—ED.]

M.H. Poincare has pointed out, however, that we know nothing as to the mechanism of the photographic impression. We cannot consider it evident that it is the kinetic energy of the ether which produces the decomposition of the sensitive salt; and if, on the contrary, we suppose it to be due to the potential energy, all the conclusions are reversed, and Neumann's idea triumphs.

Recently a very clever physicist, M. Cotton, especially known for his skilful researches in the domain of optics, has taken up anew the study of stationary waves. He has made very precise quantitative experiments, and has demonstrated, in his turn, that it is impossible, even with spherical waves, to succeed in determining on which of the two vectors which have to be regarded in all theories of light on the subject of polarization phenomena the luminous intensity and the chemical action really depend. This question, therefore, no longer exists for those physicists who admit that luminous vibrations are electrical oscillations. Whatever, then, the hypothesis formed, whether it be electric force or, on the contrary, magnetic force which we place in the plane of polarization, the mode of propagation foreseen will always be in accord with the facts observed.

Sec. 3. THE ELECTROMAGNETIC ETHER

The idea of attributing the phenomena of electricity to perturbations produced in the medium which transmits the light is already of old standing; and the physicists who witnessed the triumph of Fresnel's theories could not fail to conceive that this fluid, which fills the whole of space and penetrates into all bodies, might also play a preponderant part in electrical actions. Some even formed too hasty hypotheses on this point; for the hour had not arrived when it was possible to place them on a sufficiently sound basis, and the known facts were not numerous enough to give the necessary precision.

The founders of modern electricity also thought it wiser to adopt, with regard to this science, the attitude taken by Newton in connection with gravitation: "In the first place to observe facts, to vary the circumstances of these as much as possible, to accompany this first work by precise measurements in order to deduce from them general laws founded solely on experiment, and to deduce from these laws, independently of all hypotheses on the nature of the forces producing the phenomena, the mathematical value of these forces—that is to say, the formula representing them. Such was the system pursued by Newton. It has, in general, been adopted in France by the scholars to whom physics owe the great progress made of late years, and it has served as my guide in all my researches on electrodynamic phenomena.... It is for this reason that I have avoided speaking of the ideas I may have on the nature of the cause of the force emanating from voltaic conductors."

Thus did Ampere express himself. The illustrious physicist rightly considered the results obtained by him through following this wise method as worthy of comparison with the laws of attraction; but he knew that when this first halting-place was reached there was still further to go, and that the evolution of ideas must necessarily continue.

"With whatever physical cause," he adds, "we may wish to connect the phenomena produced by electro-dynamic action, the formula I have obtained will always remain the expression of the facts," and he explicitly indicated that if one could succeed in deducing his formula from the consideration of the vibrations of a fluid distributed through space, an enormous step would have been taken in this department of physics. He added, however, that this research appeared to him premature, and would change nothing in the results of his work, since, to accord with facts, the hypothesis adopted would always have to agree with the formula which exactly represents them.

It is not devoid of interest to observe that Ampere himself, notwithstanding his caution, really formed some hypotheses, and recognized that electrical phenomena were governed by the laws of mechanics. Yet the principles of Newton then appeared to be unshakable.

Faraday was the first to demonstrate, by clear experiment, the influence of the media in electricity and magnetic phenomena, and he attributed this influence to certain modifications in the ether which these media enclose. His fundamental conception was to reject action at a distance, and to localize in the ether the energy whose evolution is the cause of the actions manifested, as, for example, in the discharge of a condenser.