It is, perhaps, the formula proposed by Helmholtz which best accounts for all these peculiarities. Helmholtz came to establish this formula by supposing that there is a kind of friction between the ether and matter, which, like that exercised on a pendulum, here produces a double effect, changing, on the one hand, the duration of this oscillation, and, on the other, gradually damping it. He further supposed that ponderable matter is acted on by elastic forces. The theory of Helmholtz has the great advantage of representing, not only the phenomena of dispersion, but also, as M. Carvallo has pointed out, the laws of rotatory polarization, its dispersion and other phenomena, among them the dichroism of the rotatory media discovered by M.
Cotton.
In the establishment of these theories, the language of ordinary optics has always been employed. The phenomena are looked upon as due to mechanical deformations or to movements governed by certain forces.
The electromagnetic theory leads, as we have seen, to the employment of other images. M.H. Poincare, and, after him, Helmholtz, have both proposed electromagnetic theories of dispersion. On examining things closely, it will be found that there are not, in truth, in the two ways of regarding the problem, two equivalent translations of exterior reality. The electrical theory gives us to understand, much better than the mechanical one, that _in vacuo_ the dispersion ought to be strictly null, and this absence of dispersion appears to be confirmed with extraordinary precision by astronomical observations. Thus the observation, often repeated, and at different times of year, proves that in the case of the star Algol, the light of which takes at least four years to reach us, no sensible difference in coloration accompanies the changes in brilliancy.
-- 2. THE THEORY OF LORENTZ
Purely mechanical considerations have therefore failed to give an entirely satisfactory interpretation of the phenomena in which even the simplest relations between matter and the ether appear. They would, evidently, be still more insufficient if used to explain certain effects produced on matter by light, which could not, without grave difficulties, be attributed to movement; for instance, the phenomena of electrification under the influence of certain radiations, or, again, chemical reactions such as photographic impressions.
The problem had to be approached by another road. The electromagnetic theory was a step in advance, but it comes to a standstill, so to speak, at the moment when the ether penetrates into matter. If we wish to go deeper into the inwardness of the phenomena, we must follow, for example, Professor Lorentz or Dr Larmor, and look with them for a mode of representation which appears, besides, to be a natural consequence of the fundamental ideas forming the basis of Hertz"s experiments.
The moment we look upon a wave in the ether as an electromagnetic wave, a molecule which emits light ought to be considered as a kind of excitant. We are thus led to suppose that in each radiating molecule there are one or several electrified particles, animated with a to-and-fro movement round their positions of equilibrium, and these particles are certainly identical with those electrons the existence of which we have already admitted for so many other reasons.
In the simplest theory, we will imagine an electron which may be displaced from its position of equilibrium in all directions, and is, in this displacement, submitted to attractions which communicate to it a vibration like a pendulum. These movements are equivalent to tiny currents, and the mobile electron, when animated with a considerable velocity, must be sensitive to the action of the magnet which modifies the form of the trajectory and the value of the period. This almost direct consequence was perceived by Lorentz, and it led him to the new idea that radiations emitted by a body ought to be modified by the action of a strong electromagnet.
An experiment enabled this prevision to be verified. It was made, as is well known, as early as 1896 by Zeeman; and the discovery produced a legitimate sensation. When a flame is subjected to the action of a magnetic field, a brilliant line is decomposed in conditions more or less complex which an attentive study, however, allows us to define.
According to whether the observation is made in a plane normal to the magnetic field or in the same direction, the line transforms itself into a triplet or doublet, and the new lines are polarized rectilinearly or circularly.
These are the precise phenomena which the calculation foretells: the a.n.a.lysis of the modifications undergone by the light supplies, moreover, valuable information on the electron itself. From the direction of the circular vibrations of the greatest frequency we can determine the sign of the electric charge in motion and we find it to be negative. But, further than this, from the variation of the period we can calculate the relation of the force acting on the electron to its material ma.s.s, and, in addition, the relation of the charge to the ma.s.s. We then find for this relation precisely that value which we have already met with so many times. Such a coincidence cannot be fortuitous, and we have the right to believe that the electron revealed by the luminous wave which emanates from it, is really the same as the one made known to us by the study of the cathode rays and of the radioactive substances.
However, the elementary theory does not suffice to interpret the complications which later experiments have revealed. The physicists most qualified to effect measurements in these delicate optical questions--M. Cornu, Mr Preston, M. Cotton, MM. Becquerel and Deslandres, M. Broca, Professor Michelson, and others--have pointed out some remarkable peculiarities. Thus in some cases the number of the component rays dissociated by the magnetic field may be very considerable.
The great modification brought to a radiation by the Zeeman effect may, besides, combine itself with other phenomena, and alter the light in a still more complicated manner. A pencil of polarized light, as demonstrated by Signori Macaluzo and Corbino, undergoes, in a magnetic field, modifications with regard to absorption and speed of propagation.
Some ingenious researches by M. Becquerel and M. Cotton have perfectly elucidated all these complications from an experimental point of view.
It would not be impossible to link together all these phenomena without adopting the electronic hypothesis, by preserving the old optical equations as modified by the terms relating to the action of the magnetic field. This has actually been done in some very remarkable work by M. Voigt, but we may also, like Professor Lorentz, look for more general theories, in which the essential image of the electrons shall be preserved, and which will allow all the facts revealed by experiment to be included.
We are thus led to the supposition that there is not in the atom one vibrating electron only, but that there is to be found in it a dynamical system comprising several material points which may be subjected to varied movements. The neutral atom may therefore be considered as composed of an immovable princ.i.p.al portion positively charged, round which move, like satellites round a planet, several negative electrons of very inferior ma.s.s. This conclusion leads us to an interpretation in agreement with that which other phenomena have already suggested.
These electrons, which thus have a variable velocity, generate around themselves a transverse electromagnetic wave which is propagated with the velocity of light; for the charged particle becomes, as soon as it experiences a change of speed, the centre of a radiation. Thus is explained the phenomenon of the emission of radiations. In the same way, the movement of electrons may be excited or modified by the electrical forces which exist in any pencil of light they receive, and this pencil may yield up to them a part of the energy it is carrying.
This is the phenomenon of absorption.
Professor Lorentz has not contented himself with thus explaining all the mechanism of the phenomena of emission and absorption. He has endeavoured to rediscover, by starting with the fundamental hypothesis, the quant.i.tative laws discovered by thermodynamics. He succeeds in showing that, agreeably to the law of Kirchhoff, the relation between the emitting and the absorbing power must be independent of the special properties of the body under observation, and he thus again meets with the laws of Planck and of Wien: unfortunately the calculation can only be made in the case of great wave-lengths, and grave difficulties exist. Thus it cannot be very clearly explained why, by heating a body, the radiation is displaced towards the side of the short wave-lengths, or, if you will, why a body becomes luminous from the moment its temperature has reached a sufficiently high degree. On the other hand, by calculating the energy of the vibrating particles we are again led to attribute to these particles the same const.i.tution as that of the electrons.
It is in the same way possible, as Professor Lorentz has shown, to give a very satisfactory explanation of the thermo-electric phenomena by supposing that the number of liberated electrons which exist in a given metal at a given temperature has a determined value varying with each metal, and is, in the case of each body, a function of the temperature. The formula obtained, which is based on these hypotheses, agrees completely with the cla.s.sic results of Clausius and of Lord Kelvin. Finally, if we recollect that the phenomena of electric and calorific conductivity are perfectly interpreted by the hypothesis of electrons, it will no longer be possible to contest the importance of a theory which allows us to group together in one synthesis so many facts of such diverse origins.
If we study the conditions under which a wave excited by an electron"s variations in speed can be transmitted, they again bring us face to face, and generally, with the results pointed out by the ordinary electromagnetic theory. Certain peculiarities, however, are not absolutely the same. Thus the theory of Lorentz, as well as that of Maxwell, leads us to foresee that if an insulating ma.s.s be caused to move in a magnetic field normally to its lines of force, a displacement will be produced in this ma.s.s a.n.a.logous to that of which Faraday and Maxwell admitted the existence in the dielectric of a charged condenser. But M.H. Poincare has pointed out that, according as we adopt one or other of these authors" points of view, so the value of the displacement differs. This remark is very important, for it may lead to an experiment which would enable us to make a definite choice between the two theories.
To obtain the displacement estimated according to Lorentz, we must multiply the displacement calculated according to Hertz by a factor representing the relation between the difference of the specific inductive capacities of the dielectric and of a vacuum, and the first of these powers. If therefore we take as dielectric the air of which the specific inductive capacity is perceptibly the same as that of a vacuum, the displacement, according to the idea of Lorentz, will be null; while, on the contrary, according to Hertz, it will have a finite value. M. Blondlot has made the experiment. He sent a current of air into a condenser placed in a magnetic field, and was never able to notice the slightest trace of electrification. No displacement, therefore, is effected in the dielectric. The experiment being a negative one, is evidently less convincing than one giving a positive result, but it furnishes a very powerful argument in favour of the theory of Lorentz.
This theory, therefore, appears very seductive, yet it still raises objections on the part of those who oppose to it the principles of ordinary mechanics. If we consider, for instance, a radiation emitted by an electron belonging to one material body, but absorbed by another electron in another body, we perceive immediately that, the propagation not being instantaneous, there can be no compensation between the action and the reaction, which are not simultaneous; and the principle of Newton thus seems to be attacked. In order to preserve its integrity, it has to be admitted that the movements in the two material substances are compensated by that of the ether which separates these substances; but this conception, although in tolerable agreement with the hypothesis that the ether and matter are not of different essence, involves, on a closer examination, suppositions hardly satisfactory as to the nature of movements in the ether.
For a long time physicists have admitted that the ether as a whole must be considered as being immovable and capable of serving, so to speak, as a support for the axes of Galileo, in relation to which axes the principle of inertia is applicable,--or better still, as M.
Painleve has shown, they alone allow us to render obedience to the principle of causality.
But if it were so, we might apparently hope, by experiments in electromagnetism, to obtain absolute motion, and to place in evidence the translation of the earth relatively to the ether. But all the researches attempted by the most ingenious physicists towards this end have always failed, and this tends towards the idea held by many geometricians that these negative results are not due to imperfections in the experiments, but have a deep and general cause. Now Lorentz has endeavoured to find the conditions in which the electromagnetic theory proposed by him might agree with the postulate of the complete impossibility of determining absolute motion. It is necessary, in order to realise this concord, to imagine that a mobile system contracts very slightly in the direction of its translation to a degree proportioned to the square of the ratio of the velocity of transport to that of light. The electrons themselves do not escape this contraction, although the observer, since he partic.i.p.ates in the same motion, naturally cannot notice it. Lorentz supposes, besides, that all forces, whatever their origin, are affected by a translation in the same way as electromagnetic forces. M. Langevin and M. H.
Poincare have studied this same question and have noted with precision various delicate consequences of it. The singularity of the hypotheses which we are thus led to construct in no way const.i.tutes an argument against the theory of Lorentz; but it has, we must acknowledge, discouraged some of the more timid partisans of this theory.[48]
[Footnote 48: An objection not here noticed has lately been formulated with much frankness by Professor Lorentz himself. It is one of the pillars of his theory that only the negative electrons move when an electric current pa.s.ses through a metal, and that the positive electrons (if any such there be) remain motionless. Yet in the experiment known as Hall"s, the current is deflected by the magnetic field to one side of the strip in certain metals, and to the opposite side in others. This seems to show that in certain cases the positive electrons move instead of the negative, and Professor Lorentz confesses that up to the present he can find no valid argument against this. See _Archives Neerlandaises_ 1906, parts 1 and 2.--ED.]
-- 3. THE Ma.s.s OF ELECTRONS
Other conceptions, bolder still, are suggested by the results of certain interesting experiments. The electron affords us the possibility of considering inertia and ma.s.s to be no longer a fundamental notion, but a consequence of the electromagnetic phenomena.
Professor J.J. Thomson was the first to have the clear idea that a part, at least, of the inertia of an electrified body is due to its electric charge. This idea was taken up and precisely stated by Professor Max Abraham, who, for the first time, was led to regard seriously the seemingly paradoxical notion of ma.s.s as a function of velocity. Consider a small particle bearing a given electric charge, and let us suppose that this particle moves through the ether. It is, as we know, equivalent to a current proportional to its velocity, and it therefore creates a magnetic field the intensity of which is likewise proportional to its velocity: to set it in motion, therefore, there must be communicated to it over and above the expenditure corresponding to the acquisition of its ordinary kinetic energy, a quant.i.ty of energy proportional to the square of its velocity.
Everything, therefore, takes place as if, by the fact of electrification, its capacity for kinetic energy and its material ma.s.s had been increased by a certain constant quant.i.ty. To the ordinary ma.s.s may be added, if you will, an electromagnetic ma.s.s.
This is the state of things so long as the speed of the translation of the particle is not very great, but they are no longer quite the same when this particle is animated with a movement whose rapidity becomes comparable to that with which light is propagated.
The magnetic field created is then no longer a field in repose, but its energy depends, in a complicated manner, on the velocity, and the apparent increase in the ma.s.s of the particle itself becomes a function of the velocity. More than this, this increase may not be the same for the same velocity, but varies according to whether the acceleration is parallel with or perpendicular to the direction of this velocity. In other words, there seems to be a longitudinal; and a transversal ma.s.s which need not be the same.
All these results would persist even if the material ma.s.s were very small relatively to the electromagnetic ma.s.s; and the electron possesses some inertia even if its ordinary ma.s.s becomes slighter and slighter. The apparent ma.s.s, it can be easily shown, increases indefinitely when the velocity with which the electrified particle is animated tends towards the velocity of light, and thus the work necessary to communicate such a velocity to an electron would be infinite. It is in consequence impossible that the speed of an electron, in relation to the ether, can ever exceed, or even permanently attain to, 300,000 kilometres per second.
All the facts thus predicted by the theory are confirmed by experiment. There is no known process which permits the direct measurement of the ma.s.s of an electron, but it is possible, as we have seen, to measure simultaneously its velocity and the relation of the electric charge to its ma.s.s. In the case of the cathode rays emitted by radium, these measurements are particularly interesting, for the reason that the rays which compose a pencil of cathode rays are animated by very different speeds, as is shown by the size of the stain produced on a photographic plate by a pencil of them at first very constricted and subsequently dispersed by the action of an electric or magnetic field. Professor Kaufmann has effected some very careful experiments by a method he terms the method of crossed spectra, which consists in superposing the deviations produced by a magnetic and an electric field respectively acting in directions at right angles one to another. He has thus been enabled by working _in vacuo_ to register the very different velocities which, starting in the case of certain rays from about seven-tenths of the velocity of light, attain in other cases to ninety-five hundredths of it.
It is thus noted that the ratio of charge to ma.s.s--which for ordinary speeds is constant and equal to that already found by so many experiments--diminishes slowly at first, and then very rapidly when the velocity of the ray increases and approaches that of light. If we represent this variation by a curve, the shape of this curve inclines us to think that the ratio tends toward zero when the velocity tends towards that of light.
All the earlier experiments have led us to consider that the electric charge was the same for all electrons, and it can hardly be conceived that this charge can vary with the velocity. For in order that the relation, of which one of the terms remains fixed, should vary, the other term necessarily cannot remain constant. The experiments of Professor Kaufmann, therefore, confirm the previsions of Max Abraham"s theory: the ma.s.s depends on the velocity, and increases indefinitely in proportion as this velocity approaches that of light. These experiments, moreover, allow the numerical results of the calculation to be compared with the values measured. This very satisfactory comparison shows that the apparent total ma.s.s is sensibly equal to the electromagnetic ma.s.s; the material ma.s.s of the electron is therefore nil, and the whole of its ma.s.s is electromagnetic.
Thus the electron must be looked upon as a simple electric charge devoid of matter. Previous examination has led us to attribute to it a ma.s.s a thousand times less that that of the atom of hydrogen, and a more attentive study shows that this ma.s.s was fict.i.tious. The electromagnetic phenomena which are produced when the electron is set in motion or a change effected in its velocity, simply have the effect, as it were, of simulating inertia, and it is the inertia due to the charge which has caused us to be thus deluded.
The electron is therefore simply a small volume determined at a point in the ether, and possessing special properties;[49] this point is propagated with a velocity which cannot exceed that of light. When this velocity is constant, the electron creates around it in its pa.s.sage an electric and a magnetic field; round this electrified centre there exists a kind of wake, which follows it through the ether and does not become modified so long as the velocity remains invariable. If other electrons follow the first within a wire, their pa.s.sage along the wire will be what is called an electric current.
[Footnote 49: This cannot be said to be yet completely proved. _Cf_.
Sir Oliver Lodge, _Electrons_, London, 1906, p. 200.--ED.]
When the electron is subjected to an acceleration, a transverse wave is produced, and an electromagnetic radiation is generated, of which the character may naturally change with the manner in which the speed varies. If the electron has a sufficiently rapid periodical movement, this wave is a light wave; while if the electron stops suddenly, a kind of pulsation is transmitted through the ether, and thus we obtain Rontgen rays.
-- 4. NEW VIEWS ON THE CONSt.i.tUTION OF THE ETHER AND OF MATTER
New and valuable information is thus afforded us regarding the properties of the ether, but will this enable us to construct a material representation of this medium which fills the universe, and so to solve a problem which has baffled, as we have seen, the prolonged efforts of our predecessors?
Certain scholars seem to have cherished this hope. Dr. Larmor in particular, as we have seen, has proposed a most ingenious image, but one which is manifestly insufficient. The present tendency of physicists rather tends to the opposite view; since they consider matter as a very complex object, regarding which we wrongly imagine ourselves to be well informed because we are so much accustomed to it, and its singular properties end by seeming natural to us. But in all probability the ether is, in its objective reality, much more simple, and has a better right to be considered as fundamental.
We cannot therefore, without being very illogical, define the ether by material properties, and it is useless labour, condemned beforehand to sterility, to endeavour to determine it by other qualities than those of which experiment gives us direct and exact knowledge.
The ether is defined when we know, in all its points, and in magnitude and in direction, the two fields, electric and magnetic, which may exist in it. These two fields may vary; we speak from habit of a movement propagated in the ether, but the phenomenon within the reach of experiment is the propagation of these variations.
Since the electrons, considered as a modification of the ether symmetrically distributed round a point, perfectly counterfeit that inertia which is the fundamental property of matter, it becomes very tempting to suppose that matter itself is composed of a more or less complex a.s.semblage of electrified centres in motion.
This complexity is, in general, very great, as is demonstrated by the examination of the luminous spectra produced by the atoms, and it is precisely because of the compensations produced between the different movements that the essential properties of matter--the law of the conservation of inertia, for example--are not contrary to the hypothesis.
The forces of cohesion thus would be due to the mutual attractions which occur in the electric and magnetic fields produced in the interior of bodies; and it is even conceivable that there may be produced, under the influence of these actions, a tendency to determine orientation, that is to say, that a reason can be seen why matter may be crystallised.[50]
[Footnote 50: The reader should, however, be warned that a theory has lately been put forth which attempts to account for crystallisation on purely mechanical grounds. See Messrs Barlow and Pope"s "Development of the Atomic Theory" in the _Transactions of the Chemical Society_, 1906.--ED.]