All that appears, at first sight, a little artificial. In particular, this deformation of electrons seems quite hypothetical. But the thing may be presented otherwise, so as to avoid putting this hypothesis of deformation at the foundation of the reasoning. Consider the electrons as material points and ask how their ma.s.s should vary as function of the velocity not to contravene the principle of relativity. Or, still better, ask what should be their acceleration under the influence of an electric or magnetic field, that this principle be not violated and that we come back to the ordinary laws when we suppose the velocity very slight. We shall find that the variations of this ma.s.s, or of these accelerations, must be _as if_ the electron underwent the Lorentz deformation.

V

_Kaufmann's Experiment_

We have before us, then, two theories: one where the electrons are indeformable, this is that of Abraham; the other where they undergo the Lorentz deformation. In both cases, their ma.s.s increases with the velocity, becoming infinite when this velocity becomes equal to that of light; but the law of the variation is not the same. The method employed by Kaufmann to bring to light the law of variation of the ma.s.s seems therefore to give us an experimental means of deciding between the two theories.

Unhappily, his first experiments were not sufficiently precise for that; so he decided to repeat them with more precautions, and measuring with great care the intensity of the fields. Under their new form _they are in favor of the theory of Abraham_. Then the principle of relativity would not have the rigorous value we were tempted to attribute to it; there would no longer be reason for believing the positive electrons denuded of real ma.s.s like the negative electrons. However, before definitely adopting this conclusion, a little reflection is necessary.

The question is of such importance that it is to be wished Kaufmann's experiment were repeated by another experimenter.[17] Unhappily, this experiment is very delicate and could be carried out successfully only by a physicist of the same ability as Kaufmann. All precautions have been properly taken and we hardly see what objection could be made.

[17] At the moment of going to press we learn that M. Bucherer has repeated the experiment, taking new precautions, and that he has obtained, contrary to Kaufmann, results confirming the views of Lorentz.

There is one point however to which I wish to draw attention: that is to the measurement of the electrostatic field, a measurement upon which all depends. This field was produced between the two armatures of a condenser; and, between these armatures, there was to be made an extremely perfect vacuum, in order to obtain a complete isolation. Then the difference of potential of the two armatures was measured, and the field obtained by dividing this difference by the distance apart of the armatures. That supposes the field uniform; is this certain? Might there not be an abrupt fall of potential in the neighborhood of one of the armatures, of the negative armature, for example? There may be a difference of potential at the meeting of the metal and the vacuum, and it may be that this difference is not the same on the positive side and on the negative side; what would lead me to think so is the electric valve effects between mercury and vacuum. However slight the probability that it is so, it seems that it should be considered.

VI

_The Principle of Inertia_

In the new dynamics, the principle of inertia is still true, that is to say that an _isolated_ electron will have a straight and uniform motion.

At least this is generally a.s.sumed; however, Lindemann has made objections to this view; I do not wish to take part in this discussion, which I can not here expound because of its too difficult character. In any case, slight modifications to the theory would suffice to shelter it from Lindemann's objections.

We know that a body submerged in a fluid experiences, when in motion, considerable resistance, but this is because our fluids are viscous; in an ideal fluid, perfectly free from viscosity, the body would stir up behind it a liquid hill, a sort of wake; upon departure, a great effort would be necessary to put it in motion, since it would be necessary to move not only the body itself, but the liquid of its wake. But, the motion once acquired, it would perpetuate itself without resistance, since the body, in advancing, would simply carry with it the perturbation of the liquid, without the total vis viva of the liquid augmenting. Everything would happen therefore as if its inertia was augmented. An electron advancing in the ether would behave in the same way: around it, the ether would be stirred up, but this perturbation would accompany the body in its motion; so that, for an observer carried along with the electron, the electric and magnetic fields accompanying this electron would appear invariable, and would change only if the velocity of the electron varied. An effort would therefore be necessary to put the electron in motion, since it would be necessary to create the energy of these fields; on the contrary, once the movement acquired, no effort would be necessary to maintain it, since the created energy would only have to go along behind the electron as a wake. This energy, therefore, could only augment the inertia of the electron, as the agitation of the liquid augments that of the body submerged in a perfect fluid. And anyhow, the negative electrons at least have no other inertia except that.

In the hypothesis of Lorentz, the vis viva, which is only the energy of the ether, is not proportional to _v_^{2}. Doubtless if _v_ is very slight, the vis viva is sensibly proportional to _v_^{2}, the quant.i.ty of motion sensibly proportional to _v_, the two ma.s.ses sensibly constant and equal to each other. But _when the velocity tends toward the velocity of light, the vis viva, the quant.i.ty of motion and the two ma.s.ses increase beyond all limit_.

In the hypothesis of Abraham, the expressions are a little more complicated; but what we have just said remains true in essentials.

So the ma.s.s, the quant.i.ty of motion, the vis viva become infinite when the velocity is equal to that of light.

Thence results that _no body can attain in any way a velocity beyond that of light_. And in fact, in proportion as its velocity increases, its ma.s.s increases, so that its inertia opposes to any new increase of velocity a greater and greater obstacle.

A question then suggests itself: let us admit the principle of relativity; an observer in motion would not have any means of perceiving his own motion. If therefore no body in its absolute motion can exceed the velocity of light, but may approach it as nearly as you choose, it should be the same concerning its relative motion with reference to our observer. And then we might be tempted to reason as follows: The observer may attain a velocity of 200,000 kilometers; the body in its relative motion with reference to the observer may attain the same velocity; its absolute velocity will then be 400,000 kilometers, which is impossible, since this is beyond the velocity of light. This is only a seeming, which vanishes when account is taken of how Lorentz evaluates local time.

VII

_The Wave of Acceleration_

When an electron is in motion, it produces a perturbation in the ether surrounding it; if its motion is straight and uniform, this perturbation reduces to the wake of which we have spoken in the preceding section.

But it is no longer the same, if the motion be curvilinear or varied.

The perturbation may then be regarded as the superposition of two others, to which Langevin has given the names _wave of velocity_ and _wave of acceleration_. The wave of velocity is only the wave which happens in uniform motion.

As to the wave of acceleration, this is a perturbation altogether a.n.a.logous to light waves, which starts from the electron at the instant when it undergoes an acceleration, and which is then propagated by successive spherical waves with the velocity of light. Whence follows: in a straight and uniform motion, the energy is wholly conserved; but, when there is an acceleration, there is loss of energy, which is dissipated under the form of luminous waves and goes out to infinity across the ether.

However, the effects of this wave of acceleration, in particular the corresponding loss of energy, are in most cases negligible, that is to say not only in ordinary mechanics and in the motions of the heavenly bodies, but even in the radium rays, where the velocity is very great without the acceleration being so. We may then confine ourselves to applying the laws of mechanics, putting the force equal to the product of acceleration by ma.s.s, this ma.s.s, however, varying with the velocity according to the laws explained above. We then say the motion is _quasi-stationary_.

It would not be the same in all cases where the acceleration is great, of which the chief are the following:

1 In incandescent gases certain electrons take an oscillatory motion of very high frequency; the displacements are very small, the velocities are finite, and the accelerations very great; energy is then communicated to the ether, and this is why these gases radiate light of the same period as the oscillations of the electron;

2 Inversely, when a gas receives light, these same electrons are put in swing with strong accelerations and they absorb light;

3 In the Hertz discharger, the electrons which circulate in the metallic ma.s.s undergo, at the instant of the discharge, an abrupt acceleration and take then an oscillatory motion of high frequency.

Thence results that a part of the energy radiates under the form of Hertzian waves;

4 In an incandescent metal, the electrons enclosed in this metal are impelled with great velocity; upon reaching the surface of the metal, which they can not get through, they are reflected and thus undergo a considerable acceleration. This is why the metal emits light. The details of the laws of the emission of light by dark bodies are perfectly explained by this hypothesis;

5 Finally when the cathode rays strike the anticathode, the negative electrons, const.i.tuting these rays, which are impelled with very great velocity, are abruptly arrested. Because of the acceleration they thus undergo, they produce undulations in the ether. This, according to certain physicists, is the origin of the Rontgen rays, which would only be light rays of very short wave-length.

CHAPTER III

THE NEW MECHANICS AND ASTRONOMY

I

_Gravitation_

Ma.s.s may be defined in two ways:

1 By the quotient of the force by the acceleration; this is the true definition of the ma.s.s, which measures the inertia of the body.

2 By the attraction the body exercises upon an exterior body, in virtue of Newton's law. We should therefore distinguish the ma.s.s coefficient of inertia and the ma.s.s coefficient of attraction. According to Newton's law, there is rigorous proportionality between these two coefficients.

But that is demonstrated only for velocities to which the general principles of dynamics are applicable. Now, we have seen that the ma.s.s coefficient of inertia increases with the velocity; should we conclude that the ma.s.s coefficient of attraction increases likewise with the velocity and remains proportional to the coefficient of inertia, or, on the contrary, that this coefficient of attraction remains constant? This is a question we have no means of deciding.

On the other hand, if the coefficient of attraction depends upon the velocity, since the velocities of two bodies which mutually attract are not in general the same, how will this coefficient depend upon these two velocities?

Upon this subject we can only make hypotheses, but we are naturally led to investigate which of these hypotheses would be compatible with the principle of relativity. There are a great number of them; the only one of which I shall here speak is that of Lorentz, which I shall briefly expound.

Consider first electrons at rest. Two electrons of the same sign repel each other and two electrons of contrary sign attract each other; in the ordinary theory, their mutual actions are proportional to their electric charges; if therefore we have four electrons, two positive _A_ and _A'_, and two negative _B_ and _B'_, the charges of these four being the same in absolute value, the repulsion of _A_ for _A'_ will be, at the same distance, equal to the repulsion of _B_ for _B'_ and equal also to the attraction of _A_ for _B'_, or of _A'_ for _B_. If therefore _A_ and _B_ are very near each other, as also _A'_ and _B'_, and we examine the action of the system _A_ + _B_ upon the system _A'_ + _B'_, we shall have two repulsions and two attractions which will exactly compensate each other and the resulting action will be null.

Now, material molecules should just be regarded as species of solar systems where circulate the electrons, some positive, some negative, and _in such a way that the algebraic sum of all the charges is null_. A material molecule is therefore wholly a.n.a.logous to the system _A_ + _B_ of which we have spoken, so that the total electric action of two molecules one upon the other should be null.

But experiment shows us that these molecules attract each other in consequence of Newtonian gravitation; and then we may make two hypotheses: we may suppose gravitation has no relation to the electrostatic attractions, that it is due to a cause entirely different, and is simply something additional; or else we may suppose the attractions are not proportional to the charges and that the attraction exercised by a charge +1 upon a charge -1 is greater than the mutual repulsion of two +1 charges, or two -1 charges.

In other words, the electric field produced by the positive electrons and that which the negative electrons produce might be superposed and yet remain distinct. The positive electrons would be more sensitive to the field produced by the negative electrons than to the field produced by the positive electrons; the contrary would be the case for the negative electrons. It is clear that this hypothesis somewhat complicates electrostatics, but that it brings back into it gravitation.

This was, in sum, Franklin's hypothesis.

What happens now if the electrons are in motion? The positive electrons will cause a perturbation in the ether and produce there an electric and magnetic field. The same will be the case for the negative electrons.

The electrons, positive as well as negative, undergo then a mechanical impulsion by the action of these different fields. In the ordinary theory, the electromagnetic field, due to the motion of the positive electrons, exercises, upon two electrons of contrary sign and of the same absolute charge, equal actions with contrary sign. We may then without inconvenience not distinguish the field due to the motion of the positive electrons and the field due to the motion of the negative electrons and consider only the algebraic sum of these two fields, that is to say the resulting field.

In the new theory, on the contrary, the action upon the positive electrons of the electromagnetic field due to the positive electrons follows the ordinary laws; it is the same with the action upon the negative electrons of the field due to the negative electrons. Let us now consider the action of the field due to the positive electrons upon the negative electrons (or inversely); it will still follow the same laws, but _with a different coefficient_. Each electron is more sensitive to the field created by the electrons of contrary name than to the field created by the electrons of the same name.