This example will suffice to make my thought understood; I could cite many others. Thus who would suspect, in reading the pages devoted to magnetic rotary polarization, that there is an identity between optical and magnetic phenomena?
One must not then flatter himself that he can avoid all contradiction; to that it is necessary to be resigned. In fact, two contradictory theories, provided one does not mingle them, and if one does not seek in them the basis of things, may both be useful instruments of research; and perhaps the reading of Maxwell would be less suggestive if he had not opened up to us so many new and divergent paths.
The fundamental idea, however, is thus a little obscured. So far is this the case that in the majority of popularized versions it is the only point completely left aside.
I feel, then, that the better to make its importance stand out, I ought to explain in what this fundamental idea consists. But for that a short digression is necessary.
The Mechanical Explanation of Physical Phenomena.—There is in every physical phenomenon a certain number of parameters which experiment reaches directly and allows us to measure. I shall call these the parametersq.
Observation then teaches us the laws of the variations of these parameters; and these laws can generally be put in the form of differential equations, which connect the parametersqwith the time.
What is it necessary to do to give a mechanical interpretation of such a phenomenon?
One will try to explain it either by the motions of ordinary matter, or by those of one or more hypothetical fluids.
These fluids will be considered as formed of a very great number of isolated moleculesm.
When shall we say, then, that we have a complete mechanical explanation of the phenomenon? It will be, on the one hand, when we know the differential equations satisfied by the coordinates of these hypothetical moleculesm, equations which, moreover, must conform to the principles of dynamics; and, on the other hand, when we know the relations that define the coordinates of the moleculesmas functions of the parametersqaccessible to experiment.
These equations, as I have said, must conform to the principles of dynamics, and, in particular, to the principle of the conservation of energy and the principle of least action.
The first of these two principles teaches us that the total energy is constant and that this energy is divided into two parts:
1º The kinetic energy, orvis viva, which depends on the masses of the hypothetical moleculesm, and their velocities, and which I shall callT.
2º The potential energy, which depends only on the coordinates of these molecules and which I shall callU. It is thesumof the two energiesTandUwhich is constant.
What now does the principle of least action tell us? It tells us that to pass from the initial position occupied at the instantt0to the final position occupied at the instantt1, the system must take such a path that, in the interval of time that elapses between the two instantst0andt1, the average value of 'the action' (that is to say, of thedifferencebetween the two energiesTandU) shall be as small as possible.
If the two functionsTandUare known, this principle suffices to determine the equations of motion.
Among all the possible ways of passing from one position to another, there is evidently one for which the average value of the action is less than for any other. There is, moreover, only one; and it results from this that the principle of least action suffices to determine the path followed and consequently the equations of motion.
Thus we obtain what are called the equations of Lagrange.
In these equations, the independent variables are the coordinates of the hypothetical moleculesm; but I now suppose that one takes as variables the parametersqdirectly accessible to experiment.
The two parts of the energy must then be expressed as functions of the parametersqand of their derivatives. They will evidently appear under this form to the experimenter. The latter will naturally try to define the potential and the kinetic energy by the aid of quantities that he can directly observe.[6]
That granted, the system will always go from one position to another by a path such that the average action shall be a minimum.
It matters little thatTandUare now expressed by the aid of the parametersqand their derivatives; it matters little that it is also by means of these parameters that we define the initial and final positions; the principle of least action remains always true.
Now here again, of all the paths that lead from one position to another, there is one for which the average action is a minimum, and there is only one. The principle of least action suffices, then, to determine the differential equations which define the variations of the parametersq.
The equations thus obtained are another form of the equations of Lagrange.
To form these equations we need to know neither the relations that connect the parametersqwith the coordinates of the hypothetical molecules, nor the masses of these molecules, nor the expression ofUas a function of the coordinates of these molecules.
All we need to know is the expression ofUas a function of the parameters, and that ofTas a function of the parametersqand their derivatives, that is, the expressions of the kinetic and of the potential energy as functions of the experimental data.
Then we shall have one of two things: either for a suitablechoice of the functionsTandU, the equations of Lagrange, constructed as we have just said, will be identical with the differential equations deduced from experiments; or else there will exist no functionsTandU, for which this agreement takes place. In the latter case it is clear that no mechanical explanation is possible.
Thenecessarycondition for a mechanical explanation to be possible is therefore that we can choose the functionsTandUin such a way as to satisfy the principle of least action, which involves that of the conservation of energy.
This condition, moreover, issufficient. Suppose, in fact, that we have found a functionUof the parametersq, which represents one of the parts of the energy; that another part of the energy, which we shall represent byT, is a function of the parametersqand their derivatives, and that it is a homogeneous polynomial of the second degree with respect to these derivatives; and finally that the equations of Lagrange, formed by means of these two functions,TandU, conform to the data of the experiment.
What is necessary in order to deduce from this a mechanical explanation? It is necessary thatUcan be regarded as the potential energy of a system andTas thevis vivaof the same system.
There is no difficulty as toU, but canTbe regarded as thevis vivaof a material system?
It is easy to show that this is always possible, and even in an infinity of ways. I will confine myself to referring for more details to the preface of my work, 'Électricité et optique.'
Thus if the principle of least action can not be satisfied, no mechanical explanation is possible; if it can be satisfied, there is not only one, but an infinity, whence it follows that as soon as there is one there is an infinity of others.
One more observation.
Among the quantities that experiment gives us directly, we shall regard some as functions of the coordinates of our hypothetical molecules; these are our parametersq. We shall look upon the others as dependent not only on the coordinates, but on the velocities, or, what comes to the same thing, on the derivativesof the parametersq, or as combinations of these parameters and their derivatives.
And then a question presents itself: among all these quantities measured experimentally, which shall we choose to represent the parametersq? Which shall we prefer to regard as the derivatives of these parameters? This choice remains arbitrary to a very large extent; but, for a mechanical explanation to be possible, it suffices if we can make the choice in such a way as to accord with the principle of least action.
And then Maxwell asked himself whether he could make this choice and that of the two energiesTandU, in such a way that the electrical phenomena would satisfy this principle. Experiment shows us that the energy of an electromagnetic field is decomposed into two parts, the electrostatic energy and the electrodynamic energy. Maxwell observed that if we regard the first as representing the potential energyU, the second as representing the kinetic energyT; if, moreover, the electrostatic charges of the conductors are considered as parametersqand the intensities of the currents as the derivatives of other parametersq; under these conditions, I say, Maxwell observed that the electric phenomena satisfy the principle of least action. Thenceforth he was certain of the possibility of a mechanical explanation.
If he had explained this idea at the beginning of his book instead of relegating it to an obscure part of the second volume, it would not have escaped the majority of readers.
If, then, a phenomenon admits of a complete mechanical explanation, it will admit of an infinity of others, that will render an account equally well of all the particulars revealed by experiment.
And this is confirmed by the history of every branch of physics; in optics, for instance, Fresnel believed vibration to be perpendicular to the plane of polarization; Neumann regarded it as parallel to this plane. An 'experimentum crucis' has long been sought which would enable us to decide between these two theories, but it has not been found.
In the same way, without leaving the domain of electricity, we may ascertain that the theory of two fluids and that of thesingle fluid both account in a fashion equally satisfactory for all the observed laws of electrostatics.
All these facts are easily explicable, thanks to the properties of the equations of Lagrange which I have just recalled.
It is easy now to comprehend what is Maxwell's fundamental idea.
To demonstrate the possibility of a mechanical explanation of electricity, we need not preoccupy ourselves with finding this explanation itself; it suffices us to know the expression of the two functionsTandU, which are the two parts of energy, to form with these two functions the equations of Lagrange and then to compare these equations with the experimental laws.
Among all these possible explanations, how make a choice for which the aid of experiment fails us? A day will come perhaps when physicists will not interest themselves in these questions, inaccessible to positive methods, and will abandon them to the metaphysicians. This day has not yet arrived; man does not resign himself so easily to be forever ignorant of the foundation of things.
Our choice can therefore be further guided only by considerations where the part of personal appreciation is very great; there are, however, solutions that all the world will reject because of their whimsicality, and others that all the world will prefer because of their simplicity.
In what concerns electricity and magnetism, Maxwell abstains from making any choice. It is not that he systematically disdains all that is unattainable by positive methods; the time he has devoted to the kinetic theory of gases sufficiently proves that. I will add that if, in his great work, he develops no complete explanation, he had previously attempted to give one in an article in thePhilosophical Magazine. The strangeness and the complexity of the hypotheses he had been obliged to make had led him afterwards to give this up.
The same spirit is found throughout the whole work. What is essential, that is to say what must remain common to all theories, is made prominent; all that would only be suitable to a particular theory is nearly always passed over in silence. Thus the reader finds himself in the presence of a form almost devoidof matter, which he is at first tempted to take for a fugitive shadow not to be grasped. But the efforts to which he is thus condemned force him to think and he ends by comprehending what was often rather artificial in the theoretic constructs he had previously only wondered at.
The history of electrodynamics is particularly instructive from our point of view.
Ampère entitled his immortal work, 'Théorie des phénomènes électrodynamiques,uniquementfondée sur l'expérience.' He therefore imagined that he had madenohypothesis, but he had made them, as we shall soon see; only he made them without being conscious of it.
His successors, on the other hand, perceived them, since their attention was attracted by the weak points in Ampère's solution. They made new hypotheses, of which this time they were fully conscious; but how many times it was necessary to change them before arriving at the classic system of to-day which is perhaps not yet final; this we shall see.
I. Ampere's Theory.—When Ampère studied experimentally the mutual actions of currents, he operated and he only could operate with closed currents.
It was not that he denied the possibility of open currents. If two conductors are charged with positive and negative electricity and brought into communication by a wire, a current is established going from one to the other, which continues until the two potentials are equal. According to the ideas of Ampère's time this was an open current; the current was known to go from the first conductor to the second, it was not seen to return from the second to the first.
So Ampère considered as open currents of this nature, for example, the currents of discharge of condensers; but he could not make them the objects of his experiments because their duration is too short.
Another sort of open current may also be imagined. I suppose two conductors,AandB, connected by a wireAMB. Small conducting masses in motion first come in contact with theconductorB, take from it an electric charge, leave contact withBand move along the pathBNA, and, transporting with them their charge, come into contact withAand give to it their charge, which returns then toBalong the wireAMB.
Now there we have in a sense a closed circuit, since the electricity describes the closed circuitBNAMB; but the two parts of this current are very different. In the wireAMB, the electricity is displaced through a fixed conductor, like a voltaic current, overcoming an ohmic resistance and developing heat; we say that it is displaced by conduction. In the partBNA, the electricity is carried by a moving conductor; it is said to be displaced by convection.
If then the current of convection is considered as altogether analogous to the current of conduction, the circuitBNAMBis closed; if, on the contrary, the convection current is not 'a true current' and, for example, does not act on the magnet, there remains only the conduction currentAMB, which is open.
For example, if we connect by a wire the two poles of a Holtz machine, the charged rotating disc transfers the electricity by convection from one pole to the other, and it returns to the first pole by conduction through the wire.
But currents of this sort are very difficult to produce with appreciable intensity. With the means at Ampère's disposal, we may say that this was impossible.
To sum up, Ampère could conceive of the existence of two kinds of open currents, but he could operate on neither because they were not strong enough or because their duration was too short.
Experiment therefore could only show him the action of a closed current on a closed current, or, more accurately, the action of a closed current on a portion of a current, because a current can be made to describe a closed circuit composed of a moving part and a fixed part. It is possible then to study the displacements of the moving part under the action of another closed current.
On the other hand, Ampère had no means of studying the action of an open current, either on a closed current or another open current.
1.The Case of Closed Currents.—In the case of the mutual action of two closed currents, experiment revealed to Ampère remarkably simple laws.
I recall rapidly here those which will be useful to us in the sequel:
1ºIf the intensity of the currents is kept constant, and if the two circuits, after having undergone any deformations and displacements whatsoever, return finally to their initial positions, the total work of the electrodynamic actions will be null.
In other words, there is anelectrodynamic potentialof the two circuits, proportional to the product of the intensities, and depending on the form and relative position of the circuits; the work of the electrodynamic actions is equal to the variation of this potential.
2º The action of a closed solenoid is null.
3º The action of a circuitCon another voltaic circuitC´depends only on the 'magnetic field' developed by this circuit. At each point in space we can in fact define in magnitude and direction a certain force calledmagnetic force, which enjoys the following properties:
(a) The force exercised byCon a magnetic pole is applied to that pole and is equal to the magnetic force multiplied by the magnetic mass of that pole;
(b) A very short magnetic needle tends to take the direction of the magnetic force, and the couple to which it tends to reduce is proportional to the magnetic force, the magnetic moment of the needle and the sine of the dip of the needle;
(c) If the circuitCis displaced, the work of the electrodynamic action exercised byConC´will be equal to the increment of the 'flow of magnetic force' which passes through the circuit.
2.Action of a Closed Current on a Portion of Current.—Ampère not having been able to produce an open current, properly so called, had only one way of studying the action of a closed current on a portion of current.
This was by operating on a circuitCcomposed of two parts, the one fixed, the other movable. The movable part was, for instance, a movable wire αβ whose extremities α and β couldslide along a fixed wire. In one of the positions of the movable wire, the end α rested on theAof the fixed wire and the extremity β on the pointBof the fixed wire. The current circulated from α to β, that is to say, fromAtoBalong the movable wire, and then it returned fromBtoAalong the fixed wire.This current was therefore closed.
In a second position, the movable wire having slipped, the extremity α rested on another pointA´of the fixed wire, and the extremity β on another pointB´of the fixed wire. The current circulated then from α to β, that is to say fromA´toB´along the movable wire, and it afterwards returned fromB´toB, then fromBtoA, then finally fromAtoA´, always following the fixed wire. The current was therefore also closed.
If a like current is subjected to the action of a closed currentC, the movable part will be displaced just as if it were acted upon by a force. Ampèreassumesthat the apparent force to which this movable partABseems thus subjected, representing the action of theCon the portion αβ of the current, is the same as if αβ were traversed by an open current, stopping at α and β, in place of being traversed by a closed current which after arriving at β returns to α through the fixed part of the circuit.
This hypothesis seems natural enough, and Ampère made it unconsciously; neverthelessit is not necessary, since we shall see further on that Helmholtz rejected it. However that may be, it permitted Ampère, though he had never been able to produce an open current, to enunciate the laws of the action of a closed current on an open current, or even on an element of current.
The laws are simple:
1º The force which acts on an element of current is applied to this element; it is normal to the element and to the magnetic force, and proportional to the component of this magnetic force which is normal to the element.
2º The action of a closed solenoid on an element of current is null.
But the electrodynamic potential has disappeared, that is to say that, when a closed current and an open current, whose intensities have been maintained constant, return to their initial positions, the total work is not null.
3.Continuous Rotations.—Among electrodynamic experiments, the most remarkable are those in which continuous rotations are produced and which are sometimes calledunipolar inductionexperiments. A magnet may turn about its axis; a current passes first through a fixed wire, enters the magnet by the poleN, for example, passes through half the magnet, emerges by a sliding contact and reenters the fixed wire.
The magnet then begins to rotate continuously without being able ever to attain equilibrium; this is Faraday's experiment.
How is it possible? If it were a question of two circuits of invariable form, the oneCfixed, the otherC´movable about an axis, this latter could never take on continuous rotation; in fact there is an electrodynamic potential; there must therefore be necessarily a position of equilibrium when this potential is a maximum.
Continuous rotations are therefore possible only when the circuitC´is composed of two parts: one fixed, the other movable about an axis, as is the case in Faraday's experiment. Here again it is convenient to draw a distinction. The passage from the fixed to the movable part, or inversely, may take place either by simple contact (the same point of the movable part remaining constantly in contact with the same point of the fixed part), or by a sliding contact (the same point of the movable part coming successively in contact with diverse points of the fixed part).
It is only in the second case that there can be continuous rotation. This is what then happens: The system tends to take a position of equilibrium; but, when at the point of reaching that position, the sliding contact puts the movable part in communication with a new point of the fixed part; it changes the connections, it changes therefore the conditions of equilibrium, so that the position of equilibrium fleeing, so to say, before the system which seeks to attain it, rotation may take place indefinitely.
Ampère assumes that the action of the circuit on the movable part ofC´is the same as if the fixed part ofC´did not exist, and therefore as if the current passing through the movable part were open.
He concludes therefore that the action of a closed on an open current, or inversely that of an open current on a closed current, may give rise to a continuous rotation.
But this conclusion depends on the hypothesis I have enunciated and which, as I said above, is not admitted by Helmholtz.
4.Mutual Action of Two Open Currents.—In what concerns the mutual actions of two open currents, and in particular that of two elements of current, all experiment breaks down. Ampère has recourse to hypothesis. He supposes:
1º That the mutual action of two elements reduces to a force acting along their join;
2º That the action of two closed currents is the resultant of the mutual actions of their diverse elements, which are besides the same as if these elements were isolated.
What is remarkable is that here again Ampère makes these hypotheses unconsciously.
However that may be, these two hypotheses, together with the experiments on closed currents, suffice to determine completely the law of the mutual action of two elements. But then most of the simple laws we have met in the case of closed currents are no longer true.
In the first place, there is no electrodynamic potential; nor was there any, as we have seen, in the case of a closed current acting on an open current.
Next there is, properly speaking, no magnetic force.
And, in fact, we have given above three different definitions of this force:
1º By the action on a magnetic pole;
2º By the director couple which orientates the magnetic needle;
3º By the action on an element of current.
But in the case which now occupies us, not only these three definitions are no longer in harmony, but each has lost its meaning, and in fact:
1º A magnetic pole is no longer acted upon simply by a single force applied to this pole. We have seen in fact that the force due to the action of an element of current on a pole is not applied to the pole, but to the element; it may moreover be replaced by a force applied to the pole and by a couple;
2º The couple which acts on the magnetic needle is no longer a simple director couple, for its moment with respect to the axis of the needle is not null. It breaks up into a director couple, properly so called, and a supplementary couple which tends to produce the continuous rotation of which we have above spoken;
3º Finally the force acting on an element of current is not normal to this element.
In other words,the unity of the magnetic force has disappeared.
Let us see in what this unity consists. Two systems which exercise the same action on a magnetic pole will exert also the same action on an indefinitely small magnetic needle, or on an element of current placed at the same point of space as this pole.
Well, this is true if these two systems contain only closed currents; this would no longer be true if these two systems contained open currents.
It suffices to remark, for instance, that, if a magnetic pole is placed atAand an element atB, the direction of the element being along the prolongation of the sectAB, this element which will exercise no action on this pole will, on the other hand, exercise an action either on a magnetic needle placed at the pointA, or on an element of current placed at the pointA.
5.Induction.—We know that the discovery of electrodynamic induction soon followed the immortal work of Ampère.
As long as it is only a question of closed currents there is no difficulty, and Helmholtz has even remarked that the principle of the conservation of energy is sufficient for deducing the laws of induction from the electrodynamic laws of Ampère. But always on one condition, as Bertrand has well shown; that we make besides a certain number of hypotheses.
The same principle again permits this deduction in the case of open currents, although of course we can not submit the result to the test of experiment, since we can not produce such currents.
If we try to apply this mode of analysis to Ampère's theory of open currents, we reach results calculated to surprise us.
In the first place, induction can not be deduced from the variation of the magnetic field by the formula well known to savants and practicians, and, in fact, as we have said, properly speaking there is no longer a magnetic field.
But, further, if a circuitCis subjected to the induction of a variable voltaic systemS, if this systemSbe displaced and deformed in any way whatever, so that the intensity of the currents of this system varies according to any law whatever, but that after these variations the system finally returns to its initial situation, it seems natural to suppose that themeanelectromotive force induced in the circuitCis null.
This is true if the circuitCis closed and if the systemScontains only closed currents. This would no longer be true, if one accepts the theory of Ampère, if there were open currents. So that not only induction will no longer be the variation of the flow of magnetic force, in any of the usual senses of the word, but it can not be represented by the variation of anything whatever.
II. Theory of Helmholtz.—I have dwelt upon the consequences of Ampère's theory, and of his method of explaining open currents.
It is difficult to overlook the paradoxical and artificial character of the propositions to which we are thus led. One can not help thinking 'that can not be so.'
We understand therefore why Helmholtz was led to seek something else.
Helmholtz rejects Ampère's fundamental hypothesis, to wit, that the mutual action of two elements of current reduces to a force along their join. He assumes that an element of current is not subjected to a single force, but to a force and a couple. It is just this which gave rise to the celebrated polemic between Bertrand and Helmholtz.
Helmholtz replaces Ampère's hypothesis by the following: two elements always admit of an electrodynamic potential depending solely on their position and orientation; and the work of the forces that they exercise, one on the other, is equal to the variation of this potential. Thus Helmholtz can no more do without hypothesis than Ampère; but at least he does not make one without explicitly announcing it.
In the case of closed currents, which are alone accessible to experiment, the two theories agree.
In all other cases they differ.
In the first place, contrary to what Ampère supposed, the forcewhich seems to act on the movable portion of a closed current is not the same as would act upon this movable portion if it were isolated and constituted an open current.
Let us return to the circuitC´, of which we spoke above, and which was formed of a movable wire αβ sliding on a fixed wire. In the only experiment that can be made, the movable portion αβ is not isolated, but is part of a closed circuit. When it passes fromABtoA´B´, the total electrodynamic potential varies for two reasons:
1º It undergoes a first increase because the potential ofA´B´with respect to the circuitCis not the same as that ofAB;
2º It takes a second increment because it must be increased by the potentials of the elementsAA´,BB´with respect toC.
It is thisdoubleincrement which represents the work of the force to which the portionABseems subjected.
If, on the contrary, αβ were isolated, the potential would undergo only the first increase, and this first increment alone would measure the work of the force which acts onAB.
In the second place, there could be no continuous rotation without sliding contact, and, in fact, that, as we have seenà proposof closed currents, is an immediate consequence of the existence of an electrodynamic potential.
In Faraday's experiment, if the magnet is fixed and if the part of the current exterior to the magnet runs along a movable wire, that movable part may undergo a continuous rotation. But this does not mean to say that if the contacts of the wire with the magnet were suppressed, and anopencurrent were to run along the wire, the wire would still take a movement of continuous rotation.
I have just said in fact that anisolatedelement is not acted upon in the same way as a movable element making part of a closed circuit.
Another difference: The action of a closed solenoid on a closed current is null according to experiment and according to the two theories. Its action on an open current would be null according to Ampère; it would not be null according to Helmholtz. From this follows an important consequence. We have given above three definitions of magnetic force. The third hasno meaning here since an element of current is no longer acted upon by a single force. No more has the first any meaning. What, in fact, is a magnetic pole? It is the extremity of an indefinite linear magnet. This magnet may be replaced by an indefinite solenoid. For the definition of magnetic force to have any meaning, it would be necessary that the action exercised by an open current on an indefinite solenoid should depend only on the position of the extremity of this solenoid, that is to say, that the action on a closed solenoid should be null. Now we have just seen that such is not the case.
On the other hand, nothing prevents our adopting the second definition, which is founded on the measurement of the director couple which tends to orientate the magnetic needle.
But if it is adopted, neither the effects of induction nor the electrodynamic effects will depend solely on the distribution of the lines of force in this magnetic field.
III. Difficulties Raised by These Theories.—The theory of Helmholtz is in advance of that of Ampère; it is necessary, however, that all the difficulties should be smoothed away. In the one as in the other, the phrase 'magnetic field' has no meaning, or, if we give it one, by a more or less artificial convention, the ordinary laws so familiar to all electricians no longer apply; thus the electromotive force induced in a wire is no longer measured by the number of lines of force met by this wire.
And our repugnance does not come alone from the difficulty of renouncing inveterate habits of language and of thought. There is something more. If we do not believe in action at a distance, electrodynamic phenomena must be explained by a modification of the medium. It is precisely this modification that we call 'magnetic field.' And then the electrodynamic effects must depend only on this field.
All these difficulties arise from the hypothesis of open currents.
IV. Maxwell's Theory.—Such were the difficulties raised by the dominant theories when Maxwell appeared, who with a stroke of the pen made them all vanish. To his mind, in fact, all currents are closed currents. Maxwell assumes that if in a dielectric the electric field happens to vary, this dielectric becomes the seat of a particular phenomenon, acting on thegalvanometer like a current, and which he callscurrent of displacement.
If then two conductors bearing contrary charges are put in communication by a wire, in this wire during the discharge there is an open current of conduction; but there are produced at the same time in the surrounding dielectric, currents of displacement which close this current of conduction.
We know that Maxwell's theory leads to the explanation of optical phenomena, which would be due to extremely rapid electrical oscillations.
At that epoch such a conception was only a bold hypothesis, which could be supported by no experiment.
At the end of twenty years, Maxwell's ideas received the confirmation of experiment. Hertz succeeded in producing systems of electric oscillations which reproduce all the properties of light, and only differ from it by the length of their wave; that is to say as violet differs from red. In some measure he made the synthesis of light.
It might be said that Hertz has not demonstrated directly Maxwell's fundamental idea, the action of the current of displacement on the galvanometer. This is true in a sense. What he has shown in sum is that electromagnetic induction is not propagated instantaneously as was supposed; but with the speed of light.
But to suppose there is no current of displacement, and induction is propagated with the speed of light; or to suppose that the currents of displacement produce effects of induction, and that the induction is propagated instantaneously,comes to the same thing.
This can not be seen at the first glance, but it is proved by an analysis of which I must not think of giving even a summary here.
V. Rowland's Experiment.—But as I have said above, there are two kinds of open conduction currents. There are first the currents of discharge of a condenser or of any conductor whatever.
There are also the cases in which electric discharges describea closed contour, being displaced by conduction in one part of the circuit and by convection in the other part.
For open currents of the first sort, the question might be considered as solved; they were closed by the currents of displacement.
For open currents of the second sort, the solution appeared still more simple. It seemed that if the current were closed, it could only be by the current of convection itself. For that it sufficed to assume that a 'convection current,' that is to say a charged conductor in motion, could act on the galvanometer.
But experimental confirmation was lacking. It appeared difficult in fact to obtain a sufficient intensity even by augmenting as much as possible the charge and the velocity of the conductors. It was Rowland, an extremely skillful experimenter, who first triumphed over these difficulties. A disc received a strong electrostatic charge and a very great speed of rotation. An astatic magnetic system placed beside the disc underwent deviations.
The experiment was made twice by Rowland, once in Berlin, once in Baltimore. It was afterwards repeated by Himstedt. These physicists even announced that they had succeeded in making quantitative measurements.
In fact, for twenty years Rowland's law was admitted without objection by all physicists. Besides everything seemed to confirm it. The spark certainly does produce a magnetic effect. Now does it not seem probable that the discharge by spark is due to particles taken from one of the electrodes and transferred to the other electrode with their charge? Is not the very spectrum of the spark, in which we recognize the lines of the metal of the electrode, a proof of it? The spark would then be a veritable current of convection.
On the other hand, it is also admitted that in an electrolyte the electricity is carried by the ions in motion. The current in an electrolyte would therefore be also a current of convection; now, it acts on the magnetic needle.
The same for cathode rays. Crookes attributed these rays to a very subtile matter charged with electricity and moving with a very great velocity. He regarded them, in other words, as currents of convection. Now these cathode rays aredeviated by the magnet. In virtue of the principle of action and reaction, they should in turn deviate the magnetic needle. It is true that Hertz believed he had demonstrated that the cathode rays do not carry electricity, and that they do not act on the magnetic needle. But Hertz was mistaken. First of all, Perrin succeeded in collecting the electricity carried by these rays, electricity of which Hertz denied the existence; the German scientist appears to have been deceived by effects due to the action of X-rays, which were not yet discovered. Afterwards, and quite recently, the action of the cathode rays on the magnetic needle has been put in evidence.
Thus all these phenomena regarded as currents of convection, sparks, electrolytic currents, cathode rays, act in the same manner on the galvanometer and in conformity with Rowland's law.
VI. Theory of Lorentz.—We soon went farther. According to the theory of Lorentz, currents of conduction themselves would be true currents of convection. Electricity would remain inseparably connected with certain material particles calledelectrons. The circulation of these electrons through bodies would produce voltaic currents. And what would distinguish conductors from insulators would be that the one could be traversed by these electrons while the others would arrest their movements.
The theory of Lorentz is very attractive. It gives a very simple explanation of certain phenomena which the earlier theories, even Maxwell's in its primitive form, could not explain in a satisfactory way; for example, the aberration of light, the partial carrying away of luminous waves, magnetic polarization and the Zeeman effect.
Some objections still remained. The phenomena of an electric system seemed to depend on the absolute velocity of translation of the center of gravity of this system, which is contrary to the idea we have of the relativity of space. Supported by M. Crémieu, M. Lippmann has presented this objection in a striking form. Imagine two charged conductors with the same velocity of translation; they are relatively at rest. However, each of them being equivalent to a current of convection, they ought to attract one another, and by measuring this attraction we could measure their absolute velocity.
"No!" replied the partisans of Lorentz. "What we could measure in that way is not their absolute velocity, but their relative velocitywith respect to the ether, so that the principle of relativity is safe."
Whatever there may be in these latter objections, the edifice of electrodynamics, at least in its broad lines, seemed definitively constructed. Everything was presented under the most satisfactory aspect. The theories of Ampère and of Helmholtz, made for open currents which no longer existed, seemed to have no longer anything but a purely historic interest, and the inextricable complications to which these theories led were almost forgotten.
This quiescence has been recently disturbed by the experiments of M. Crémieu, which for a moment seemed to contradict the result previously obtained by Rowland.
But fresh researches have not confirmed them, and the theory of Lorentz has victoriously stood the test.
The history of these variations will be none the less instructive; it will teach us to what pitfalls the scientist is exposed, and how he may hope to escape them.