Facts conscientiously observed lead by induction to the enunciation of a certain number of laws or general hypotheses which are the principles already referred to. These princ.i.p.al hypotheses are, in the eyes of a physicist, legitimate generalizations, the consequences of which we shall be able at once to check by the experiments from which they issue.
Among the principles almost universally adopted until lately figure prominently those of mechanics--such as the principle of relativity, and the principle of the equality of action and reaction. We will not detail nor discuss them here, but later on we shall have an opportunity of pointing out how recent theories on the phenomena of electricity have shaken the confidence of physicists in them and have led certain scholars to doubt their absolute value.
The principle of Lavoisier, or principle of the conservation of ma.s.s, presents itself under two different aspects according to whether ma.s.s is looked upon as the coefficient of the inertia of matter or as the factor which intervenes in the phenomena of universal attraction, and particularly in gravitation. We shall see when we treat of these theories, how we have been led to suppose that inertia depended on velocity and even on direction. If this conception were exact, the principle of the invariability of ma.s.s would naturally be destroyed.
Considered as a factor of attraction, is ma.s.s really indestructible?
A few years ago such a question would have seemed singularly audacious. And yet the law of Lavoisier is so far from self-evident that for centuries it escaped the notice of physicists and chemists.
But its great apparent simplicity and its high character of generality, when enunciated at the end of the eighteenth century, rapidly gave it such an authority that no one was able to any longer dispute it unless he desired the reputation of an oddity inclined to paradoxical ideas.
It is important, however, to remark that, under fallacious metaphysical appearances, we are in reality using empty words when we repeat the aphorism, "Nothing can be lost, nothing can be created," and deduce from it the indestructibility of matter. This indestructibility, in truth, is an experimental fact, and the principle depends on experiment. It may even seem, at first sight, more singular than not that the weight of a bodily system in a given place, or the quotient of this weight by that of the standard ma.s.s--that is to say, the ma.s.s of these bodies--remains invariable, both when the temperature changes and when chemical reagents cause the original materials to disappear and to be replaced by new ones. We may certainly consider that in a chemical phenomenon annihilations and creations of matter are really produced; but the experimental law teaches us that there is compensation in certain respects.
The discovery of the radioactive bodies has, in some sort, rendered popular the speculations of physicists on the phenomena of the disaggregation of matter. We shall have to seek the exact meaning which ought to be given to the experiments on the emanation of these bodies, and to discover whether these experiments really imperil the law of Lavoisier.
For some years different experimenters have also effected many very precise measurements of the weight of divers bodies both before and after chemical reactions between these bodies. Two highly experienced and cautious physicists, Professors Landolt and Heydweiller, have not hesitated to announce the sensational result that in certain circ.u.mstances the weight is no longer the same after as before the reaction. In particular, the weight of a solution of salts of copper in water is not the exact sum of the joint weights of the salt and the water. Such experiments are evidently very delicate; they have been disputed, and they cannot be considered as sufficient for conviction.
It follows nevertheless that it is no longer forbidden to regard the law of Lavoisier as only an approximate law; according to Sandford and Ray, this approximation would be about 1/2,400,000. This is also the result reached by Professor Poynting in experiments regarding the possible action of temperature on the weight of a body; and if this be really so, we may rea.s.sure ourselves, and from the point of view of practical application may continue to look upon matter as indestructible.
The principles of physics, by imposing certain conditions on phenomena, limit after a fashion the field of the possible. Among these principles is one which, notwithstanding its importance when compared with that of universally known principles, is less familiar to some people. This is the principle of symmetry, more or less conscious applications of which can, no doubt, be found in various works and even in the conceptions of Copernican astronomers, but which was generalized and clearly enunciated for the first time by the late M. Curie. This ill.u.s.trious physicist pointed out the advantage of introducing into the study of physical phenomena the considerations on symmetry familiar to crystallographers; for a phenomenon to take place, it is necessary that a certain dissymmetry should previously exist in the medium in which this phenomenon occurs. A body, for instance, may be animated with a certain linear velocity or a speed of rotation; it may be compressed, or twisted; it may be placed in an electric or in a magnetic field; it may be affected by an electric current or by one of heat; it may be traversed by a ray of light either ordinary or polarized rectilineally or circularly, etc.:--in each case a certain minimum and characteristic dissymmetry is necessary at every point of the body in question.
This consideration enables us to foresee that certain phenomena which might be imagined _a priori_ cannot exist. Thus, for instance, it is impossible that an electric field, a magnitude directed and not superposable on its image in a mirror perpendicular to its direction, could be created at right angles to the plane of symmetry of the medium; while it would be possible to create a magnetic field under the same conditions.
This consideration thus leads us to the discovery of new phenomena; but it must be understood that it cannot of itself give us absolutely precise notions as to the nature of these phenomena, nor disclose their order of magnitude.
-- 2. THE PRINCIPLE OF THE CONSERVATION OF ENERGY
Dominating not physics alone, but nearly every other science, the principle of the conservation of energy is justly considered as the grandest conquest of contemporary thought. It shows us in a powerful light the most diverse questions; it introduces order into the most varied studies; it leads to a clear and coherent interpretation of phenomena which, without it, appear to have no connexion with each other; and it supplies precise and exact numerical relations between the magnitudes which enter into these phenomena.
The boldest minds have an instinctive confidence in it, and it is the principle which has most stoutly resisted that a.s.sault which the daring of a few theorists has lately directed to the overthrow of the general principles of physics. At every new discovery, the first thought of physicists is to find out how it accords with the principle of the conservation of energy. The application of the principle, moreover, never fails to give valuable hints on the new phenomenon, and often even suggests a complementary discovery. Up till now it seems never to have received a check, even the extraordinary properties of radium not seriously contradicting it; also the general form in which it is enunciated gives it such a suppleness that it is no doubt very difficult to overthrow.
I do not claim to set forth here the complete history of this principle, but I will endeavour to show with what pains it was born, how it was kept back in its early days and then obstructed in its development by the unfavourable conditions of the surroundings in which it appeared. It first of all came, in fact, to oppose itself to the reigning theories; but, little by little, it acted on these theories, and they were modified under its pressure; then, in their turn, these theories reacted on it and changed its primitive form.
It had to be made less wide in order to fit into the cla.s.sic frame, and was absorbed by mechanics; and if it thus became less general, it gained in precision what it lost in extent. When once definitely admitted and cla.s.sed, as it were, in the official domain of science, it endeavoured to burst its bonds and return to a more independent and larger life. The history of this principle is similar to that of all evolutions.
It is well known that the conservation of energy was, at first, regarded from the point of view of the reciprocal transformations between heat and work, and that the principle received its first clear enunciation in the particular case of the principle of equivalence. It is, therefore, rightly considered that the scholars who were the first to doubt the material nature of caloric were the precursors of R.
Mayer; their ideas, however, were the same as those of the celebrated German doctor, for they sought especially to demonstrate that heat was a mode of motion.
Without going back to early and isolated attempts like those of Daniel Bernoulli, who, in his hydrodynamics, propounded the basis of the kinetic theory of gases, or the researches of Boyle on friction, we may recall, to show how it was propounded in former times, a rather forgotten page of the _Memoire sur la Chaleur_, published in 1780 by Lavoisier and Laplace: "Other physicists," they wrote, after setting out the theory of caloric, "think that heat is nothing but the result of the insensible vibrations of matter.... In the system we are now examining, heat is the _vis viva_ resulting from the insensible movements of the molecules of a body; it is the sum of the products of the ma.s.s of each molecule by the square of its velocity.... We shall not decide between the two preceding hypotheses; several phenomena seem to support the last mentioned--for instance, that of the heat produced by the friction of two solid bodies. But there are others which are more simply explained by the first, and perhaps they both operate at once." Most of the physicists of that period, however, did not share the prudent doubts of Lavoisier and Laplace. They admitted, without hesitation, the first hypothesis; and, four years after the appearance of the _Memoire sur la Chaleur_, Sigaud de Lafond, a professor of physics of great reputation, wrote: "Pure Fire, free from all state of combination, seems to be an a.s.sembly of particles of a simple, h.o.m.ogeneous, and absolutely unalterable matter, and all the properties of this element indicate that these particles are infinitely small and free, that they have no sensible cohesion, and that they are moved in every possible direction by a continual and rapid motion which is essential to them.... The extreme tenacity and the surprising mobility of its molecules are manifestly shown by the ease with which it penetrates into the most compact bodies and by its tendency to put itself in equilibrium throughout all bodies near to it."
It must be acknowledged, however, that the idea of Lavoisier and Laplace was rather vague and even inexact on one important point. They admitted it to be evident that "all variations of heat, whether real or apparent, undergone by a bodily system when changing its state, are produced in inverse order when the system pa.s.ses back to its original state." This phrase is the very denial of equivalence where these changes of state are accompanied by external work.
Laplace, moreover, himself became later a very convinced partisan of the hypothesis of the material nature of caloric, and his immense authority, so fortunate in other respects for the development of science, was certainly in this case the cause of the r.e.t.a.r.dation of progress.
The names of Young, Rumford, Davy, are often quoted among those physicists who, at the commencement of the nineteenth century, caught sight of the new truths as to the nature of heat. To these names is very properly added that of Sadi Carnot. A note found among his papers unquestionably proves that, before 1830, ideas had occurred to him from which it resulted that in producing work an equivalent amount of heat was destroyed. But the year 1842 is particularly memorable in the history of science as the year in which Jules Robert Mayer succeeded, by an entirely personal effort, in really enunciating the principle of the conservation of energy. Chemists recall with just pride that the _Remarques sur les forces de la nature animee_, contemptuously rejected by all the journals of physics, were received and published in the _Annalen_ of Liebig. We ought never to forget this example, which shows with what difficulty a new idea contrary to the cla.s.sic theories of the period succeeds in coming to the front; but extenuating circ.u.mstances may be urged on behalf of the physicists.
Robert Mayer had a rather insufficient mathematical education, and his Memoirs, the _Remarques_, as well as the ulterior publications, _Memoire sur le mouvement organique et la nutrition_ and the _Materiaux pour la dynamique du ciel_, contain, side by side with very profound ideas, evident errors in mechanics. Thus it often happens that discoveries put forward in a somewhat vague manner by adventurous minds not overburdened by the heavy baggage of scientific erudition, who audaciously press forward in advance of their time, fall into quite intelligible oblivion until rediscovered, clarified, and put into shape by slower but surer seekers. This was the case with the ideas of Mayer. They were not understood at first sight, not only on account of their originality, but also because they were couched in incorrect language.
Mayer was, however, endowed with a singular strength of thought; he expressed in a rather confused manner a principle which, for him, had a generality greater than mechanics itself, and so his discovery was in advance not only of his own time but of half the century. He may justly be considered the founder of modern energetics.
Freed from the obscurities which prevented its being clearly perceived, his idea stands out to-day in all its imposing simplicity.
Yet it must be acknowledged that if it was somewhat denaturalised by those who endeavoured to adapt it to the theories of mechanics, and if it at first lost its sublime stamp of generality, it thus became firmly fixed and consolidated on a more stable basis.
The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the principle of the conservation of energy into mechanics, were far from useless. These ill.u.s.trious physicists succeeded in giving a more precise form to its numerous applications; and their attempts thus contributed, by reaction, to give a fresh impulse to mechanics, and allowed it to be linked to a more general order of facts. If energetics has not been able to be included in mechanics, it seems indeed that the attempt to include mechanics in energetics was not in vain.
In the middle of the last century, the explanation of all natural phenomena seemed more and more referable to the case of central forces. Everywhere it was thought that reciprocal actions between material points could be perceived, these points being attracted or repelled by each other with an intensity depending only on their distance or their ma.s.s. If, to a system thus composed, the laws of the cla.s.sical mechanics are applied, it is shown that half the sum of the product of the ma.s.ses by the square of the velocities, to which is added the work which might be accomplished by the forces to which the system would be subject if it returned from its actual to its initial position, is a sum constant in quant.i.ty.
This sum, which is the mechanical energy of the system, is therefore an invariable quant.i.ty in all the states to which it may be brought by the interaction of its various parts, and the word energy well expresses a capital property of this quant.i.ty. For if two systems are connected in such a way that any change produced in the one necessarily brings about a change in the other, there can be no variation in the characteristic quant.i.ty of the second except so far as the characteristic quant.i.ty of the first itself varies--on condition, of course, that the connexions are made in such a manner as to introduce no new force. It will thus be seen that this quant.i.ty well expresses the capacity possessed by a system for modifying the state of a neighbouring system to which we may suppose it connected.
Now this theorem of pure mechanics was found wanting every time friction took place--that is to say, in all really observable cases.
The more perceptible the friction, the more considerable the difference; but, in addition, a new phenomenon always appeared and heat was produced. By experiments which are now cla.s.sic, it became established that the quant.i.ty of heat thus created independently of the nature of the bodies is always (provided no other phenomena intervene) proportional to the energy which has disappeared.
Reciprocally, also, heat may disappear, and we always find a constant relation between the quant.i.ties of heat and work which mutually replace each other.
It is quite clear that such experiments do not prove that heat is work. We might just as well say that work is heat. It is making a gratuitous hypothesis to admit this reduction of heat to mechanism; but this hypothesis was so seductive, and so much in conformity with the desire of nearly all physicists to arrive at some sort of unity in nature, that they made it with eagerness and became unreservedly convinced that heat was an active internal force.
Their error was not in admitting this hypothesis; it was a legitimate one since it has proved very fruitful. But some of them committed the fault of forgetting that it was an hypothesis, and considered it a demonstrated truth. Moreover, they were thus brought to see in phenomena nothing but these two particular forms of energy which in their minds were easily identified with each other.
From the outset, however, it became manifest that the principle is applicable to cases where heat plays only a parasitical part. There were thus discovered, by translating the principle of equivalence, numerical relations between the magnitudes of electricity, for instance, and the magnitudes of mechanics. Heat was a sort of variable intermediary convenient for calculation, but introduced in a roundabout way and destined to disappear in the final result.
Verdet, who, in lectures which have rightly remained celebrated, defined with remarkable clearness the new theories, said, in 1862: "Electrical phenomena are always accompanied by calorific manifestations, of which the study belongs to the mechanical theory of heat. This study, moreover, will not only have the effect of making known to us interesting facts in electricity, but will throw some light on the phenomena of electricity themselves."
The eminent professor was thus expressing the general opinion of his contemporaries, but he certainly seemed to have felt in advance that the new theory was about to penetrate more deeply into the inmost nature of things. Three years previously, Rankine also had put forth some very remarkable ideas the full meaning of which was not at first well understood. He it was who comprehended the utility of employing a more inclusive term, and invented the phrase energetics. He also endeavoured to create a new doctrine of which rational mechanics should be only a particular case; and he showed that it was possible to abandon the ideas of atoms and central forces, and to construct a more general system by subst.i.tuting for the ordinary consideration of forces that of the energy which exists in all bodies, partly in an actual, partly in a potential state.
By giving more precision to the conceptions of Rankine, the physicists of the end of the nineteenth century were brought to consider that in all physical phenomena there occur apparitions and disappearances which are balanced by various energies. It is natural, however, to suppose that these equivalent apparitions and disappearances correspond to transformations and not to simultaneous creations and destructions. We thus represent energy to ourselves as taking different forms--mechanical, electrical, calorific, and chemical-- capable of changing one into the other, but in such a way that the quant.i.tative value always remains the same. In like manner a bank draft may be represented by notes, gold, silver, or bullion. The earliest known form of energy, _i.e._ work, will serve as the standard as gold serves as the monetary standard, and energy in all its forms will be estimated by the corresponding work. In each particular case we can strictly define and measure, by the correct application of the principle of the conservation of energy, the quant.i.ty of energy evolved under a given form.
We can thus arrange a machine comprising a body capable of evolving this energy; then we can force all the organs of this machine to complete an entirely closed cycle, with the exception of the body itself, which, however, has to return to such a state that all the variables from which this state depends resume their initial values except the particular variable to which the evolution of the energy under consideration is linked. The difference between the work thus accomplished and that which would have been obtained if this variable also had returned to its original value, is the measure of the energy evolved.
In the same way that, in the minds of mechanicians, all forces of whatever origin, which are capable of compounding with each other and of balancing each other, belong to the same category of beings, so for many physicists energy is a sort of ent.i.ty which we find under various aspects. There thus exists for them a world, which comes in some way to superpose itself upon the world of matter--that is to say, the world of energy, dominated in its turn by a fundamental law similar to that of Lavoisier.[5] This conception, as we have already seen, pa.s.ses the limit of experience; but others go further still. Absorbed in the contemplation of this new world, they succeed in persuading themselves that the old world of matter has no real existence and that energy is sufficient by itself to give us a complete comprehension of the Universe and of all the phenomena produced in it. They point out that all our sensations correspond to changes of energy, and that everything apparent to our senses is, in truth, energy. The famous experiment of the blows with a stick by which it was demonstrated to a sceptical philosopher that an outer world existed, only proves, in reality, the existence of energy, and not that of matter. The stick in itself is inoffensive, as Professor Ostwald remarks, and it is its _vis viva_, its kinetic energy, which is painful to us; while if we possessed a speed equal to its own, moving in the same direction, it would no longer exist so far as our sense of touch is concerned.
[Footnote 5: "Nothing is created; nothing is lost"--ED.]
On this hypothesis, matter would only be the capacity for kinetic energy, its pretended impenetrability energy of volume, and its weight energy of position in the particular form which presents itself in universal gravitation; nay, s.p.a.ce itself would only be known to us by the expenditure of energy necessary to penetrate it. Thus in all physical phenomena we should only have to regard the quant.i.ties of energy brought into play, and all the equations which link the phenomena to one another would have no meaning but when they apply to exchanges of energy. For energy alone can be common to all phenomena.
This extreme manner of regarding things is seductive by its originality, but appears somewhat insufficient if, after enunciating generalities, we look more closely into the question. From the philosophical point of view it may, moreover, seem difficult not to conclude, from the qualities which reveal, if you will, the varied forms of energy, that there exists a substance possessing these qualities. This energy, which resides in one region, and which transports itself from one spot to another, forcibly brings to mind, whatever view we may take of it, the idea of matter.
Helmholtz endeavoured to construct a mechanics based on the idea of energy and its conservation, but he had to invoke a second law, the principle of least action. If he thus succeeded in dispensing with the hypothesis of atoms, and in showing that the new mechanics gave us to understand the impossibility of certain movements which, according to the old, ought to have been but never were experimentally produced, he was only able to do so because the principle of least action necessary for his theory became evident in the case of those irreversible phenomena which alone really exist in Nature. The energetists have thus not succeeded in forming a thoroughly sound system, but their efforts have at all events been partly successful. Most physicists are of their opinion, that kinetic energy is only a particular variety of energy to which we have no right to wish to connect all its other forms.
If these forms showed themselves to be innumerable throughout the Universe, the principle of the conservation of energy would, in fact, lose a great part of its importance. Every time that a certain quant.i.ty of energy seemed to appear or disappear, it would always be permissible to suppose that an equivalent quant.i.ty had appeared or disappeared somewhere else under a new form; and thus the principle would in a way vanish. But the known forms of energy are fairly restricted in number, and the necessity of recognising new ones seldom makes itself felt. We shall see, however, that to explain, for instance, the paradoxical properties of radium and to re-establish concord between these properties and the principle of the conservation of energy, certain physicists have recourse to the hypothesis that radium borrows an unknown energy from the medium in which it is plunged. This hypothesis, however, is in no way necessary; and in a few other rare cases in which similar hypotheses have had to be set up, experiment has always in the long run enabled us to discover some phenomenon which had escaped the first observers and which corresponds exactly to the variation of energy first made evident.
One difficulty, however, arises from the fact that the principle ought only to be applied to an isolated system. Whether we imagine actions at a distance or believe in intermediate media, we must always recognise that there exist no bodies in the world incapable of acting on each other, and we can never affirm that some modification in the energy of a given place may not have its echo in some unknown spot afar off. This difficulty may sometimes render the value of the principle rather illusory.
Similarly, it behoves us not to receive without a certain distrust the extension by certain philosophers to the whole Universe, of a property demonstrated for those restricted systems which observation can alone reach. We know nothing of the Universe as a whole, and every generalization of this kind outruns in a singular fashion the limit of experiment.
Even reduced to the most modest proportions, the principle of the conservation of energy retains, nevertheless, a paramount importance; and it still preserves, if you will, a high philosophical value. M.J.
Perrin justly points out that it gives us a form under which we are experimentally able to grasp causality, and that it teaches us that a result has to be purchased at the cost of a determined effort.
We can, in fact, with M. Perrin and M. Langevin, represent this in a way which puts this characteristic in evidence by enunciating it as follows: "If at the cost of a change C we can obtain a change K, there will never be acquired at the same cost, whatever the mechanism employed, first the change K and in addition some other change, unless this latter be one that is otherwise known to cost nothing to produce or to destroy." If, for instance, the fall of a weight can be accompanied, without anything else being produced, by another transformation--the melting of a certain ma.s.s of ice, for example--it will be impossible, no matter how you set about it or whatever the mechanism used, to a.s.sociate this same transformation with the melting of another weight of ice.
We can thus, in the transformation in question, obtain an appropriate number which will sum up that which may be expected from the external effect, and can give, so to speak, the price at which this transformation is bought, measure its invariable value by a common measure (for instance, the melting of the ice), and, without any ambiguity, define the energy lost during the transformation as proportional to the ma.s.s of ice which can be a.s.sociated with it. This measure is, moreover, independent of the particular phenomenon taken as the common measure.