It has been recognized, in the first place, that the cathode rays carry with them a negative electric charge; they are deviated by a magnetic field and by an electric field; and these deviations are precisely such as these same fields would produce upon projectiles animated by a very high velocity and strongly charged with electricity. These two deviations depend upon two quant.i.ties: one the velocity, the other the relation of the electric charge of the projectile to its ma.s.s; we cannot know the absolute value of this ma.s.s, nor that of the charge, but only their relation; in fact, it is clear that if we double at the same time the charge and the ma.s.s, without changing the velocity, we shall double the force which tends to deviate the projectile, but, as its ma.s.s is also doubled, the acceleration and deviation observable will not be changed. The observation of the two deviations will give us therefore two equations to determine these two unknowns. We find a velocity of from 10,000 to 30,000 kilometers a second; as to the ratio of the charge to the ma.s.s, it is very great. We may compare it to the corresponding ratio in regard to the hydrogen ion in electrolysis; we then find that a cathodic projectile carries about a thousand times more electricity than an equal ma.s.s of hydrogen would carry in an electrolyte.

To confirm these views, we need a direct measurement of this velocity to compare with the velocity so calculated. Old experiments of J. J.

Thomson had given results more than a hundred times too small; but they were exposed to certain causes of error. The question was taken up again by Wiechert in an arrangement where the Hertzian oscillations were utilized; results were found agreeing with the theory, at least as to order of magnitude; it would be of great interest to repeat these experiments. However that may be, the theory of undulations appears powerless to account for this complex of facts.

The same calculations made with reference to the [beta] rays of radium have given velocities still greater: 100,000 or 200,000 kilometers or more yet. These velocities greatly surpa.s.s all those we know. It is true that light has long been known to go 300,000 kilometers a second; but it is not a carrying of matter, while, if we adopt the emission theory for the cathode rays, there would be material molecules really impelled at the velocities in question, and it is proper to investigate whether the ordinary laws of mechanics are still applicable to them.

II

_Ma.s.s Longitudinal and Ma.s.s Transversal_

We know that electric currents produce the phenomena of induction, in particular _self-induction_. When a current increases, there develops an electromotive force of self-induction which tends to oppose the current; on the contrary, when the current decreases, the electromotive force of self-induction tends to maintain the current. The self-induction therefore opposes every variation of the intensity of the current, just as in mechanics the inertia of a body opposes every variation of its velocity.

_Self-induction is a veritable inertia._ Everything happens as if the current could not establish itself without putting in motion the surrounding ether and as if the inertia of this ether tended, in consequence, to keep constant the intensity of this current. It would be requisite to overcome this inertia to establish the current, it would be necessary to overcome it again to make the current cease.

A cathode ray, which is a rain of projectiles charged with negative electricity, may be likened to a current; doubtless this current differs, at first sight at least, from the currents of ordinary conduction, where the matter does not move and where the electricity circulates through the matter. This is a _current of convection_, where the electricity, attached to a material vehicle, is carried along by the motion of this vehicle. But Rowland has proved that currents of convection produce the same magnetic effects as currents of conduction; they should produce also the same effects of induction. First, if this were not so, the principle of the conservation of energy would be violated; besides, Cremieu and Pender have employed a method putting in evidence _directly_ these effects of induction.

If the velocity of a cathode corpuscle varies, the intensity of the corresponding current will likewise vary; and there will develop effects of self-induction which will tend to oppose this variation. These corpuscles should therefore possess a double inertia: first their own proper inertia, and then the apparent inertia, due to self-induction, which produces the same effects. They will therefore have a total apparent ma.s.s, composed of their real ma.s.s and of a fict.i.tious ma.s.s of electromagnetic origin. Calculation shows that this fict.i.tious ma.s.s varies with the velocity, and that the force of inertia of self-induction is not the same when the velocity of the projectile accelerates or slackens, or when it is deviated; therefore so it is with the force of the total apparent inertia.

The total apparent ma.s.s is therefore not the same when the real force applied to the corpuscle is parallel to its velocity and tends to accelerate the motion as when it is perpendicular to this velocity and tends to make the direction vary. It is necessary therefore to distinguish the _total longitudinal ma.s.s_ from the _total transversal ma.s.s_. These two total ma.s.ses depend, moreover, upon the velocity. This follows from the theoretical work of Abraham.

In the measurements of which we speak in the preceding section, what is it we determine in measuring the two deviations? It is the velocity on the one hand, and on the other hand the ratio of the charge to the _total transversal ma.s.s_. How, under these conditions, can we make out in this total ma.s.s the part of the real ma.s.s and that of the fict.i.tious electromagnetic ma.s.s? If we had only the cathode rays properly so called, it could not be dreamed of; but happily we have the rays of radium which, as we have seen, are notably swifter. These rays are not all identical and do not behave in the same way under the action of an electric field and a magnetic field. It is found that the electric deviation is a function of the magnetic deviation, and we are able, by receiving on a sensitive plate radium rays which have been subjected to the action of the two fields, to photograph the curve which represents the relation between these two deviations. This is what Kaufmann has done, deducing from it the relation between the velocity and the ratio of the charge to the total apparent ma.s.s, a ratio we shall call [epsilon].

One might suppose there are several species of rays, each characterized by a fixed velocity, by a fixed charge and by a fixed ma.s.s. But this hypothesis is improbable; why, in fact, would all the corpuscles of the same ma.s.s take always the same velocity? It is more natural to suppose that the charge as well as the _real_ ma.s.s are the same for all the projectiles, and that these differ only by their velocity. If the ratio [epsilon] is a function of the velocity, this is not because the real ma.s.s varies with this velocity; but, since the fict.i.tious electromagnetic ma.s.s depends upon this velocity, the total apparent ma.s.s, alone observable, must depend upon it, though the real ma.s.s does not depend upon it and may be constant.

The calculations of Abraham let us know the law according to which the _fict.i.tious_ ma.s.s varies as a function of the velocity; Kaufmann's experiment lets us know the law of variation of the _total_ ma.s.s.

The comparison of these two laws will enable us therefore to determine the ratio of the real ma.s.s to the total ma.s.s.

Such is the method Kaufmann used to determine this ratio. The result is highly surprising: _the real ma.s.s is naught_.

This has led to conceptions wholly unexpected. What had only been proved for cathode corpuscles was extended to all bodies. What we call ma.s.s would be only semblance; all inertia would be of electromagnetic origin.

But then ma.s.s would no longer be constant, it would augment with the velocity; sensibly constant for velocities up to 1,000 kilometers a second, it then would increase and would become infinite for the velocity of light. The transversal ma.s.s would no longer be equal to the longitudinal: they would only be nearly equal if the velocity is not too great. The principle _B_ of mechanics would no longer be true.

III

_The Ca.n.a.l Rays_

At the point where we now are, this conclusion might seem premature. Can one apply to all matter what has been proved only for such light corpuscles, which are a mere emanation of matter and perhaps not true matter? But before entering upon this question, a word must be said of another sort of rays. I refer to the _ca.n.a.l rays_, the _Ka.n.a.lstrahlen_ of Goldstein.

The cathode, together with the cathode rays charged with negative electricity, emits ca.n.a.l rays charged with positive electricity. In general, these ca.n.a.l rays not being repelled by the cathode, are confined to the immediate neighborhood of this cathode, where they const.i.tute the 'chamois cushion,' not very easy to perceive; but, if the cathode is pierced with holes and if it almost completely blocks up the tube, the ca.n.a.l rays spread _back_ of the cathode, in the direction opposite to that of the cathode rays, and it becomes possible to study them. It is thus that it has been possible to show their positive charge and to show that the magnetic and electric deviations still exist, as for the cathode rays, but are much feebler.

Radium likewise emits rays a.n.a.logous to the ca.n.a.l rays, and relatively very absorbable, called [alpha] rays.

We can, as for the cathode rays, measure the two deviations and thence deduce the velocity and the ratio [epsilon]. The results are less constant than for the cathode rays, but the velocity is less, as well as the ratio [epsilon]; the positive corpuscles are less charged than the negative; or if, which is more natural, we suppose the charges equal and of opposite sign, the positive corpuscles are much the larger. These corpuscles, charged the ones positively, the others negatively, have been called _electrons_.

IV

_The Theory of Lorentz_

But the electrons do not merely show us their existence in these rays where they are endowed with enormous velocities. We shall see them in very different roles, and it is they that account for the princ.i.p.al phenomena of optics and electricity. The brilliant synthesis about to be noticed is due to Lorentz.

Matter is formed solely of electrons carrying enormous charges, and, if it seems to us neutral, this is because the charges of opposite sign of these electrons compensate each other. We may imagine, for example, a sort of solar system formed of a great positive electron, around which gravitate numerous little planets, the negative electrons, attracted by the electricity of opposite name which charges the central electron. The negative charges of these planets would balance the positive charge of this sun, so that the algebraic sum of all these charges would be naught.

All these electrons swim in the ether. The ether is everywhere identically the same, and perturbations in it are propagated according to the same laws as light or the Hertzian oscillations _in vacuo_. There is nothing but electrons and ether. When a luminous wave enters a part of the ether where electrons are numerous, these electrons are put in motion under the influence of the perturbation of the ether, and they then react upon the ether. So would be explained refraction, dispersion, double refraction and absorption. Just so, if for any cause an electron be put in motion, it would trouble the ether around it and would give rise to luminous waves, and this would explain the emission of light by incandescent bodies.

In certain bodies, the metals for example, we should have fixed electrons, between which would circulate moving electrons enjoying perfect liberty, save that of going out from the metallic body and breaking the surface which separates it from the exterior void or from the air, or from any other non-metallic body.

These movable electrons behave then, within the metallic body, as do, according to the kinetic theory of gases, the molecules of a gas within the vase where this gas is confined. But, under the influence of a difference of potential, the negative movable electrons would tend to go all to one side, and the positive movable electrons to the other. This is what would produce electric currents, and _this is why these bodies would be conductors_. On the other hand, the velocities of our electrons would be the greater the higher the temperature, if we accept the a.s.similation with the kinetic theory of gases. When one of these movable electrons encounters the surface of the metallic body, whose boundary it can not pa.s.s, it is reflected like a billiard ball which has. .h.i.t the cushion, and its velocity undergoes a sudden change of direction. But when an electron changes direction, as we shall see further on, it becomes the source of a luminous wave, and this is why hot metals are incandescent.

In other bodies, the dielectrics and the transparent bodies, the movable electrons enjoy much less freedom. They remain as if attached to fixed electrons which attract them. The farther they go away from them the greater becomes this attraction and tends to pull them back. They therefore can make only small excursions; they can no longer circulate, but only oscillate about their mean position. This is why these bodies would not be conductors; moreover they would most often be transparent, and they would be refractive, since the luminous vibrations would be communicated to the movable electrons, susceptible of oscillation, and thence a perturbation would result.

I can not here give the details of the calculations; I confine myself to saying that this theory accounts for all the known facts, and has predicted new ones, such as the Zeeman effect.

V

_Mechanical Consequences_

We now may face two hypotheses:

1 The positive electrons have a real ma.s.s, much greater than their fict.i.tious electromagnetic ma.s.s; the negative electrons alone lack real ma.s.s. We might even suppose that apart from electrons of the two signs, there are neutral atoms which have only their real ma.s.s. In this case, mechanics is not affected; there is no need of touching its laws; the real ma.s.s is constant; simply, motions are deranged by the effects of self-induction, as has always been known; moreover, these perturbations are almost negligible, except for the negative electrons which, not having real ma.s.s, are not true matter.

2 But there is another point of view; we may suppose there are no neutral atoms, and the positive electrons lack real ma.s.s just as the negative electrons. But then, real ma.s.s vanishing, either the word _ma.s.s_ will no longer have any meaning, or else it must designate the fict.i.tious electromagnetic ma.s.s; in this case, ma.s.s will no longer be constant, the transversal _ma.s.s_ will no longer be equal to the longitudinal, the principles of mechanics will be overthrown.

First a word of explanation. We have said that, for the same charge, the _total_ ma.s.s of a positive electron is much greater than that of a negative. And then it is natural to think that this difference is explained by the positive electron having, besides its fict.i.tious ma.s.s, a considerable real ma.s.s; which takes us back to the first hypothesis.

But we may just as well suppose that the real ma.s.s is null for these as for the others, but that the fict.i.tious ma.s.s of the positive electron is much the greater since this electron is much the smaller. I say advisedly: much the smaller. And, in fact, in this hypothesis inertia is exclusively electromagnetic in origin; it reduces itself to the inertia of the ether; the electrons are no longer anything by themselves; they are solely holes in the ether and around which the ether moves; the smaller these holes are, the more will there be of ether, the greater, consequently, will be the inertia of the ether.

How shall we decide between these two hypotheses? By operating upon the ca.n.a.l rays as Kaufmann did upon the [beta] rays? This is impossible; the velocity of these rays is much too slight. Should each therefore decide according to his temperament, the conservatives going to one side and the lovers of the new to the other? Perhaps, but, to fully understand the arguments of the innovators, other considerations must come in.

CHAPTER II

MECHANICS AND OPTICS

I

_Aberration_

You know in what the phenomenon of aberration, discovered by Bradley, consists. The light issuing from a star takes a certain time to go through a telescope; during this time, the telescope, carried along by the motion of the earth, is displaced. If therefore the telescope were pointed in the _true_ direction of the star, the image would be formed at the point occupied by the crossing of the threads of the network when the light has reached the objective; and this crossing would no longer be at this same point when the light reached the plane of the network.

We would therefore be led to mis-point the telescope to bring the image upon the crossing of the threads. Thence results that the astronomer will not point the telescope in the direction of the absolute velocity of the light, that is to say toward the true position of the star, but just in the direction of the relative velocity of the light with reference to the earth, that is to say toward what is called the apparent position of the star.

The velocity of light is known; we might therefore suppose that we have the means of calculating the _absolute_ velocity of the earth. (I shall soon explain my use here of the word absolute.) Nothing of the sort; we indeed know the apparent position of the star we observe; but we do not know its true position; we know the velocity of the light only in magnitude and not in direction.