The Dogma of the Indestructibility of Energy

The New Principles: Book III: The Dogma of the Indestructibility of Energy

Chapter I – The Monistic Concept of Forces and the Theory of the Conservation of Energy

1. The Conservation of Energy

The various forces of the universe were considered by the old physicists as different from, and as exhibiting no connection with each other. Heat, electricity, light, etc., seemed unrelated phenomena.

The ideas which sprang up during the second half of the last century differ much from this. After having settled that the disappearance of one force was always followed by the appearance of another, it was soon recognized that they all depended on the transformation of one indestructible entity — energy. Like matter it might change its form, but the quantity of it in the universe remained invariable. The various forces, light, heat, etc., were only different manifestations of energy.

The idea that forces might be indestructible is of fairly recent origin. The dogma of the conservation of energy only boasts, in fact, about half a century of existence. Up to the date of its discovery, science only possessed one permanent element — matter. For the last 60 years it has possessed, or has thought it possessed, a second — energy.

The principle of the conservation of energy presents itself in a form so imposing and so simple, and answers so completely to certain tendencies of the mind, that one would suppose that it must have attracted keen attention the very day it was promulgated. Quite other was its fate. For 10 years not a single scholar in the world could be found who would even consent to discuss it. In vain did its immortal author, Dr Mayer of Heilbronn, multiply his memoirs (1) and his experiments. Mayer died of despair and so unknown that when Helmholtz repeated the same discovery a few years later, taking as a basis only mathematical considerations, he did not even suspect the existence of his predecessor. The critical mind is so rare a gift that the most profound ideas and the most convincing experiments exercise no influence so long as they are not adopted by scholars enjoying the prestige of official authority.

[(1) The first paper of Mayer, “Remarks on the Forces of Inanimate Nature”, was published in 1842. His last, “Remarks on the Mechanical Equivalent of Heat” was published in 1851.]

Nevertheless, it always happens in the long run that a new idea finds a champion in some scholar possessing this prestige, and then it rapidly makes its way. As soon as the grandeur of the idea of the conservation of energy was understood by one such, it had an immediate success.

It was especially the discussion of W. Thomson (Later Lord Kelvin) and the experiments of Joule, confirming the results of Mayer on the equivalence of heat and work, which attracted the attention of specialists. The whole army of laborers of science then pounced upon this subject, and in a few years the unity and the equivalence of physical forces came to be proclaimed, though on rather narrow grounds.

This generalization proceeded from experiments which in reality did not include it. It was, in fact, deduced from the researches made to determine the rise in temperature produced by the fall of a weight to a given height into a liquid. It was noted that in order to raise by 1 degree the temperature of a kilogram of water it was necessary to let drop from a height of one meter a weight of 425 kilograms. This number 425 was called the mechanical equivalent of heat.

In this experiment and other similar ones we simply establish that the different forms of energy can be transformed into mechanical work; but nothing indicates any relationship between them. We can, by making a machine to turn by human arms, steam, the wind, electricity, etc., produce the same amount of work, although its causes are perceptibly different. To speak of the mechanical equivalent of heat only signifies that with 425 kilograms falling from a height of one meter we raise the temperature of water by 1 degree. In reality, heat or any form of energy is equivalent to work rather as a piece of 20 sous is equivalent to the pound of beef one can buy with it.

Since the part of science is much more to measure things than to define them, the acquisition of a unit of measure always realizes for it an immense progress. Thanks to the creation of a unit of energy or work, we have succeeded in stating exactly notions which were formerly very vague. When, by means of any form of energy, it is possible to produce a determined number of calories or of kilogram-meters, our minds are made up as to its magnitude. Practically it is always by means of the heat they produce, measured by the elevation of the temperature of the water of a calorimeter, that most chemical, electrical, and other forces are calculated.

To the principle of the conservation of energy others have been successively added which have allowed the laws of distribution to be clearly established. Applied at first solely to heat — that is to say, to that branch of physics called thermodynamics — they were soon extended to all forms of energy. Thus was founded a particular science, Energetic Mechanics, which we will briefly examine later on.

2. The Principles of Thermodynamics

Thermodynamics and energetic mechanics which is only the extension of the first named, rest on the three principles (1) of the conservation of energy, (2) of its distribution, or the principle of Carnot, and (3) of the law of least action.

The first, already indicated above, is formulated as follows: The quantity of energy contained in the universe is invariable.

Generalizing a little less confidently at the present time, we limit ourselves to saying that, in an isolated system, the sum of the visible energy and of the potential energy is constant. In this form the principle evidently remains unassailable, because the potential energy not being always available, we can always attribute to it the value necessary to satisfy the required ratio.

The second principle of thermodynamics, or principle of Carnot, although it has become very complicated from the introduction into it of very different things in a purely mathematical form, is nevertheless completely contained in the following enunciation given by Clausius: Heat cannot pass from a cold body to a hot without work. This is now generalized thus: The transport of energy can only be effected by a fall in tension. This signifies that energy always goes from the point where the tension is highest to that where it is lowest. The importance of the principle of Carnot dwells in this generalization. It is applicable not only to heat but to all known modes of energy — calorific, thermal, electrical, or otherwise.

This passage of energy from the point where its tension is highest to that where it is lowest is perfectly comparable to the flowing of a liquid contained in a vessel communicating by a tube with another vessel placed at a lower level. It may equally be compared to the flowing of the water of a river into the sea.

Heat foes from a heated to a cold body, and never from a cold to a heated body, by a law analogous to that which compels rivers to flow down to the sea and prevents them from flowing back to their source. To say that rivers flow down to the sea and do not retrace their course is a simple translation of the principle of Carnot.

Expressed in this way, it appears as a self-evident fact. Carnot put it into almost as simple a form, and yet physicists took nearly 25 years to grasp its full bearing. His genius-inspired idea was just to compare a fall of great heat to a fall of water, and all subsequent progress has consisted in recognizing that the various forms of energy, electricity in particular, obey, in their distribution, the laws which regulate the flow of liquids. Let us see, however, exactly what Carnot wrote: —

“The production of motive power is due, in steam engines, not to an actual consumption of calorific, but of its transport from a heated body to a cool body — that is to say, to the restoration of its equilibrium which is supposed to be broken by one cause or another, by a chemical reaction such as combustion or by some other… The motive power of heat may be compared to that of a fall of water. Both have a maximum that cannot be passed, and this irrespective of the machine employed to receive the action of the water and the substance used to receive the action of the heat. The motive power of a fall of water depends on the height and the quantity of the liquid; the motive power of heat depends likewise on the quantity of calorific used, which we will call the height of its fall — that is to say, the difference of temperature of the bodies between which is effected the exchange of calorific”.

Carnot was not an experimenter. His brief memoir is based on simple arguments, and can, in its essence, be brought down to the short passage I have quoted. And yet, by the sole fact of his principle being understood, the theoretical and practical science of the last century was entirely overturned. No physicist or chemist now enunciates a new proposition without first verifying whether it is in contradiction to the principle of Carnot. It might be said that never did so simple an idea have such profound consequences. It will forever serve to show the preponderant role of directing ideas in scientific revolution, and also how slow is the acquisition of the most simple generalization.

The second principle of thermodynamics has, in reality, much greater importance than the first. Of which, moreover, it is almost independent. Even if energy were not preserved, its distribution would always take place, at least in the immense majority of cases, in accordance with the principle of Carnot.

The generality of this principle permits it to be extended to all the phenomena in the universe. It regulates their march, and forbids them to be reversible — that is to say, it condemns them always to take the same direction, and consequently not to go backwards up the course of time. If some magic power greater than that of the demons of the mathematician Maxwell were to compel the molecular edifices to pass again into their former condition, it would slowly lead the world backward, and oblige it to retreat up the course of ages, and would thus force its inhabitants to assume successively the earlier forms in which they appeared during the chain of geological periods.

The principle of Carnot was completed by that called the principle of least action, or principle of Hamilton, which shows us the road which is follows by molecules constrained by superior force to transport themselves from one point to another. He tells us that these molecules can only take one direction, viz. the one which requires the least effort. This again is one of those principles of very great simplicity and yet immensely far-reaching. Reverting to the form given above to the principle of Carnot, that rivers descend to the sea and do not go back along their course, we may add that, by reason of the principle of least effort, rivers flow to the sea by the way which demands the least effort for the flow of water — that is to say, by the greatest slope.

Chapter II – The Energetical Explanation of Phenomena

1. The Principles of Energetic Mechanics

It is one of the principles of thermodynamics, just briefly set forth, that the science of energetic mechanics, which claims to replace the classical mechanics, has been founded.

Energetic mechanics occupies itself solely with the measurement of phenomena, and never with their interpretation. Nothing inaccessible to calculation exists. Eliminating matter and force, it studies nothing but the transformations of energy, and only knows phenomena from their energetic actions. It measures quantities of heat, magnetic fields, differences of potential, etc., and confines itself to establishing the mathematical relations between these magnitudes.

A few brief indication will suffice to show how, in this theory, the forces of the universe are conceived. The energetic theory is rather a method than a doctrine. Still it has introduced into science certain important conceptions which I will briefly state.

In energetic mechanics, energy is considered under two forms — the kinetic and the potential. The first represents energy in movement, the second energy at rest, but capable of acting when the repose ceases. Such, for instance, is the force of a coiled spring, of the weight of a wound-up clock, etc.

The potential and kinetic energy of a system may vary inversely, but their sum remains constant within the system. Kinetic energy depends on the position of the molecules and their velocities, and is proportioned to the square of these velocities. Potential energy depends solely on the position of the molecules. The principle of least action, explained above, permits the equations of movement to be established when the kinetic and potential energies are known.

2. The Quantity of Energy and Its Tension

Bringing precision into certain notions which are rather confused in the old mechanics, the energetic theory has shown that the energy of a body, whatever be the natural force to which it is related, is the product of two factors, the one tension or intensity, the other quantity. Tension regulates the direction of the transport of energy. According to the forms of energy, it is represented by a velocity, a pressure, a temperature, a height, an electromotive force, etc. By returning to the comparison of a force with the flow of a liquid which served Carnot to explain his principle, it is easy to understand the part played by these two factors — quantity and tension. In a reservoir, quantity is represented by the mass of the liquid, tension by its height above the orifices through which it escapes.

All forms of energy being known only by the work they produce, and there being nothing to differentiate the work of the various forces — electrical, mechanical, thermal, etc. — it follows that they can all be expressed by the same unit of work, viz. the kilogram-meter. For the sake of convenience others are sometimes used, but they can always be reduced to kilogram-meters. It is thus, for instance, that the joule used in electricity as the unit of work represents about one-tenth of the kilogram-meter. In the language of modern physicists, energy has become synonymous with work reckoned in kilogram-meters.

The two factors quantity and tension are magnitudes to which we can give no other definitions that their measurement. In gravity, the quantity is represented by kilograms, the tension by the number of meters in the height of the drop. Their product represents the gravitic energy. In electricity, the quantity is represented by the output of the source in coulombs, the tension by the electric pressure in volts. In kinetic energy the quantity is represented by the mass and the tension by the velocity, etc.

In a general way, therefore, if we designate by E the energy expressed in units of work, by Q the quantity, and by T the tension, we have E = Q x T. It follows that Q = E/T. The quantity is therefore represented by the energy divided by the tension. (1)

[(1) In thermal energy the name of entropy is generally given to the quotient Q/T, in which Q represents the thermal energy and T the absolute temperature. This is expressed in a more general way by the integral M/T. When a certain quantity of thermal energy passes from a heated to a cold body, its entropy diminishes, and that of the cold body increases. The entropy can be varied without changing the temperature. It is therefore a variable which under certain conditions may change in an independent manner.

Out of this notion of entropy certain physicists seem desirous of making a special physical magnitude which can be generalized in the different forms of energy. We have seen that by the artifice of expressing the most varied forms of energy in work measured by kilogram-meters all energies are made equivalent, which allows them to be added up arithmetically. But there is no basis of equivalence for the factors of which they are composed. It is therefore not possible to add up the entropies of the different energies of a body to obtain one single total entropy. It is easy to see that the factors of the different energies express things very different in reality. In thermal energy, for example, the factor tension is represented by a temperature; in kinetic energy by a velocity; in gravitic energy by a height, etc.

One can be sure that a notion is obscure when it is understood in very different ways by the scholars who make use of it. Poincare regards entropy as “a prodigiously abstract concept”, and it must be singularly so for the most celebrated physicists to comprehend it in such different fashions. This can be gathered from a long discussion published in the English journals Nature, The Electrical Review, and The Electrician, for 1900 and 1901. Eminent physicists published therein the most contradictory opinions, and seemed, moreover, astonished at their reciprocal ignorance of each other’s ideas. To engineers, the concept of entropy is a very simple matter calculable in figures because they have only applied it to the case of steam engines. To them the entropy of a body simply represents the variation (estimable in calories) of its thermal energy available for external work by degree of temperature and by kilogram of matter when heat is neither added nor taken away from it. The difficulties relative to entropy are derived from the impossibility of defining in what the different forms of energy consist. So far as electricity and heat, for instance, are concerned, one may remark with M. Lucien Poincare, “that it is impossible to establish a connection translatable into exact numerical ratios between a quantity of heat which is equivalent to a quantity of energy and a quantity of electricity which must be multiplied by a certain potential to express a certain quantity of work”.]

One finds indeed things which seem analogous in the different forms of energy, but these analogies are often very superficial. In electricity the resistance almost corresponds to mass in kinetic energy, but to what does it correspond in thermal energy? Is it the heat necessary to change the state of a body without modifying its temperature, and to simply conquer the resistance of the molecules to change? On these important points the textbooks are silent. However that may be, in all forms of energy these two elements, quantity and tension, of which the product represents the work, are always found. Without tension there could be no transmission of energy. It is especially in electricity that the difference between the two factors quantity and tension is clearly seen. The static machines in our laboratories yield electricity under a very high tension since it may reach as high as 50,000 volts; but their output is insignificant, since it never amounts to more than a few thousandths of an ampere. A galvanic battery, on the contrary, has a high yield in amperes, while the electricity issues from it at a very feeble tension hardly exceeding two volts.

The old electricians, who knew not these distinctions, thought very erroneously that the static machines in our laboratories were, by reason of the loud sparks they produced, powerful generators of electricity. The tension is enormous, but the quantity infinitesimal, so that the product of these two magnitudes represents an insignificant amount of work. It is for this reason that the sparks from these noisy machines produce insignificant results, while with industrial machines where the tension hardly exceeds 100 volts or so, but which give a high output, the physiological, calorific, and luminescent effects are considerable.

In the study of heat, the difference between the two magnitudes tension and quantity can likewise be clearly shown. Tension is represented by the temperature of a body, quantity by the number of calories it can produce. A very simple example will show the difference between the two factors.

Let us burn a match of fir-wood or a whole forest of the same tree, and the thermometer thrust into the flame of the match or into that of the forest will indicate the same temperature. It is evident, however, that the quantity of heat generated in the two cases will be far different. With the heat produced by the combustion of the match we can only bring a few drops of water to boiling point, while with the quantity of heat resulting from the combustion of the forest, we could boil several tons of the same liquid.

3. Transformation of Quantity into Tension, and Conversely

The product of the quantity by the tension — that is to say, the work — is a constant magnitude; but it is possible, without altering that product, to increase one of the factors and to diminish the other. These are operation to which commerce has recourse daily.

The hydraulic analogies given above — and to which we should always turn if we wish to thoroughly understand the distribution of energy — enable us to conceive how quantity can be transformed into tension, or conversely, without varying their total product. As regard a reservoir of liquid, for example, we can see that without varying the weight of the liquid and by simply modifying the height and width of the receptacle, we can obtain at will a very great output with very feeble pressure, or, on the other hand, a very small output with a very great pressure.

The transformation of quantity into tension, and conversely, is inconstant use in electricity. With a battery having a tension of only a few volts, but an output in amperes fairly great, it is possible, by passing the current through an induction coil, to bring the electricity to a tension of more than 20,000 volts, while greatly reducing its output. The converse operation may likewise be effected. In certain industrial installations we succeed in producing electricity under a tension of 100,000 volts, and then this tension, much too great to be of practical use, is transformed so as to obtain a great output at a feeble voltage. In all these operation, the product of the quantity by the tension — that is to say, of the coulombs by the volts — remains invariable.

Judging by their effects, we might believe that quantity and tension constitute two very different elements. They are in reality but two forms of the same thing. The transformation of quantity into tension results simply from the mode of distribution of the same energy. The converse operation will transform, on the contrary, tension into quantity. A coulomb spread over a sphere of 10,000 kilometers radius will give only a pressure of one volt. Let us spread the same quantity of electricity over a sphere of a diameter 100,000 times less — that is to say, of 100 meters, and this same quantity of electricity will produce a potential a hundred thousand times higher — that is to say, a pressure of 100,000 volts.

It would be the same for any other form of energy — for instance, light. If we possess a pencil of light, lighting feebly a surface of given extent, and wish to increase the light of a part of this surface, we have only to concentrate the pencil on a small space by means of a lens. The intensity of the part lighted will be considerably increased, but the illuminated surface will be notably reduced. By the same operation, we might increase the temperature produced by a pencil of radiant heat to the melting point of a metal. By a converse operation — that is to say, by dispersing a pencil of radiations by a prism or diverging lens — we increase the surface lighted or warmed, but reduce the intensity by the unit of surface. None of the above operations has varied the quantity of energy expended. Its distribution alone has altered.

4. The Part of Matter in Energetic Mechanics

In the above summary, we have had recourse to the principles of energetic mechanics especially. As a method of calculation they are above criticism, but we must not try to get from them an attempt at the explanation of phenomena. Moreover, the energetic theory utterly rejects such explanations. Confining its role to the measure of magnitudes subsequently connected together by equations, it denies the existence of force, ignores matter, and replaces them both by a single entity — energy, the varieties of which it limits itself to measuring.

“But then, it will be said”, writes on of the defenders of the doctrine (Prof Ostwald), “if we have to give up atoms and mechanics, what image of reality will remain to us? But we need no image and no symbol. The task of science is to establish the relations between realities — that is to say, tangible and measurable magnitudes — in such fashion that, some being given, the others are deduced from them… Hereafter there is no need to trouble ourselves about forces of which we cannot demonstrate the existence, acting between atoms of which we are not cognizant, but only to concern ourselves with the quantities of energy brought into play in the phenomena under study. These we can measure… All the equations which link together two or more phenomena of different species are necessarily equations between quantities of energy. There cannot be any other, for, besides time and space, energy is the only magnitude which is common to all orders of phenomena”.

Nor did the classical mechanics bring matter into its equations, since it only dealt with its effects, but it did not deny its existence. Energetic mechanics, which finds it simpler to ignore it than to seek to explain it, will never lead to any very high philosophical conception. Science would hardly have progresses if it had declined to try to understand what at first seemed above its reach. Tendencies of the same nature formerly existed in zoology, at the time when it was purely descriptive, and refused to deal with the origin of beings and their transformation. So long as such ideas prevailed, that science made but trifling progress; but if this narrow conception had not reigned for a long enough period, philosophical minds like Lamarck’s and Darwin’s would not have found the materials for their synthesis. It would be impossible to multiply too extensively the number of specialists whose lives are spent in weighing or measuring something. From time to time an architect appears who raises an edifice with materials which have been patiently brought together by sleepless workmen. The disciples of energetic mechanics are today accumulating documents of this kind against the day when superior minds will appear who will make good use of them.

In treating matter as a negligible quantity, energetic mechanics has only taken on its shoulder a metaphysical inheritance centuries old. For a long time it was one of the regular recreations of philosophers to prove that matter and even the universe did not exist, and to expatiate at length on these negations. These inoffensive speculations lose all interest as soon as one enters a laboratory. We are then indeed compelled to act as if matter were a very real thing with which the universe was built, and which is in consequence the substratum of phenomena. We there have to distinguish very clearly also the matter which can be weighted, and the different forms of energy — light, heat, etc. — which cannot be weighed, and are consequently added to bodies without increasing their weight.

Notwithstanding therefore all the equations of energetics, the great duality between matter and energy continued to exist. Matter might be eliminated from calculations, but this elimination did not make it vanish from reality.

The readers of my last work know how I endeavored to make this classical dichotomy vanish by showing that matter was nothing else than energy in a form which had acquired fixity. We have taken from it none of the special properties which allow is to affirm its existence as matter, but have simply shown that it constitutes a form of energy capable of transforming itself into other forms, and that it is, through its dissociation, the origin of most of the forces of the universe, notably solar heat and electricity. Far, then, from deciding on its non-existence, we have been led to consider it as the principal element of things.

Chapter III – The Degradation of Energy and Potential Energy

1. The Theory of the Degradation of Energy

The dogma of the indestructibility of energy no longer rests on very safe arguments, but it is supported by some very strong beliefs which put it above discussion. Very scarce are the scholars who, following the example of the illustrious mathematician Henri Poincare, have discovered its weakness and pointed out its uncertainties.

From the time of the earliest researches into the relations of heat and work, it was recognized that if it were possible to transform a given quantity of work into heat, we possess no means of effecting the converse operation without loss. The best steam engines do not transform into work much more than one tenth of the heat expended. Observation indeed shows that the disappearance of any form of energy is always followed by the apparition of a different energy; but this evolution is accompanied by a degradation of the original energy, which becomes less utilizable. The sole exception is perhaps gravitic energy.

The indestructibility of energy did not, then, imply its invulnerability. There would have to be several qualities of energy, of which heat would be the lowest. The different energies having an invincible tendency to transform themselves into this low form of energy, it followed that all those in the universe would finally undergo this transformation. As differences of temperature equalize themselves by diffusion, and as heat is only utilizable as energy on condition of its being able to act on bodies of lower temperature, it follows that when all particles of matter contain energy at the same low degree of tension, no exchange could take place between them. This would be the end of out universe. From a highly differentiated state, it would have passed gradually to a non-differentiated state. Its energy would not be destroyed, since by definition it is supposed to be immortal. It would become simply unusable, and would remain unutilized until the day when our world would meet with another at a lower level of energy, with which it would in consequence exchange something. In the theory which we shall now deduce from our researches, things would have a little differently.

2. Potential Energy

The concept of potential energy is only the extension of facts of elementary observation. I have already said that in the theory of conservation of energy this latter presents itself in two forms, kinetic energy or energy of movement and potential energy. In an isolated system these two forms of energy may vary in opposite directions, but their sum remains constant. If therefore we call the kinetic energy of a system C, and the potential energy P, we obtain C + P = constant.

Evidently nothing is simpler and the classic example of the weight of the wound-ip clock well illustrates this apparent simplicity. So long as the weight does not act, the kinetic energy employed in winding it up remains stored up in the potential state. So soon as the weight commences to descend, this potential energy passes into the kinetic state, and at any moment of its course the sum of the kinetic energy expended and that of the potential energy not yet used is equal to the total energy primarily employed to raise the weight.

In such elementary cases as this, there is no difficulty in distinguishing the kinetic from the potential energy; but once we go beyond these very simple examples, it becomes possible, as Poincare has shown, to separate the two forms of energy, and consequently to ascertain the total energy (chemical, electrical, etc) of a system. The formulas end by including such heterogeneous things, that energy can no longer be defined.

“If we wish”, he says in La Science et l’Hypothese, “to enunciate the principle of the conservation of energy in all its generality, and to apply it to the universe, we see it, so to speak, vanish, and there remains but this — there is something which remains constant. But is there even any sense in this?”.

Very fortunately for the progress of science, when the consequences of the principle of conservation of energy were developed, its champions did not look so closely into the matter. Disdaining objections, they established a principle which has rendered immense services by the researches of which it was the origin. What it has especially shown is that the work expended to produce a certain effect — a new chemical equilibrium, for instance — is not lost, but is recovered when the body returns to its primitive state. It is nearly thus, moreover, that the principle of the conservation of energy is now regarded. It brings us back, then, to saying that the work yielded by a spring when released is equal to the power absorbed in compressing it. And we thus stumble once more on one of those truths of commonplace obviousness which often form the web of the greatest scientific principles.

However this may be, the faculty which physicists have arrogated to themselves of considering the energy which appears to be lost as having passed into its potential state, will always remove the principle of the conservation of energy from experimental criticism. Latent potential energy plays the part of those “hidden forces” by the intervention of which the early mechanics succeeded in fitting into its equations the experiments which escaped them. The moment conservation of energy is admitted as a postulate, we must suppose that that which appears lost is to be found somewhere else, and the abyss of potential energy provides it with an inviolable shelter. But if we start from the contrary postulate, that energy can be used and lost, we are compelled to acknowledge that the second postulate would have in its favor at least as many facts as the first.

These are, moreover, barren discussions, since experiment is incapable of throwing light on this question. We had, therefore, to retain the principle of the conservation of energy until, after having penetrated further into the intra-atomic universe, it had benn clearly set forth in what way energy becomes lost. This is a point of which the solution can be dimly seen, and I will presently examine it.

It would be equally useless to dwell on facts which agree very badly or not at all with the principle of the permanence of energy, since it is enough to imagine any hypothesis whatever to make them fit in with this principle. Thus a way of explaining how the mass of a body can immensely increase with its velocity, as has been proven by experiments with radioactive particles, will certainly be found. It has indeed been explained how a permanent magnet may be for an indefinite space of time traversed by currents without its becoming heated by the friction, which would lead to the loss of its magnetism. It was enough to suppose that either it had no resistance — that is to say, to confer on it a property that the non-instantaneous nature of the propagation of light proves not to exist.

These unverifiable hypotheses have always allowed a theory to be saved so long as it is a fertile one. Many hypotheses in physics, such as that of the kinetic theory of gases, would probably quickly vanish if the experiment could throw light on them. These molecules unceasingly bustling against each other with the velocity of a cannon ball, without becoming heated, thanks to an elasticity supposed to be infinite, having perhaps but a very remote resemblance to the reality. The theory is rightly retained because it is a fruitful one, and because no possible experiment enables us to prove its inaccuracy.

We have seen how the theory of the degradation of energy and its transformation into inaccessible potential energy allows us to withdraw the principle of the conservation of energy from the criticism of experiment. This theory has satisfied the immense majority of physicists, but not all. We know what Poincare thinks of it. He is not the only one to have stated doubts. Quite recently, M. Sabatier, Dean of the Faculty of Sciences at Montpellier, propounded in an interesting inaugural lecture with the title “Is the Material Universe Eternal?”, the question whether it was quite certain that there was not a real and progressive loss of energy in the world; and more recently still, in a memoir on the degradation of energy, one of our most far-seeing physicists, M. Bernard Brunhas, expressed himself as follows: —

“What is our warrant for the statement that the universe is a limited system? If it be not so, what signify these expressions: ‘the total energy of the universe’, or the utilizable energy of the universe? To say that the total energy is preserved but that the utilizable energy diminishes, is this not formulating meaningless propositions?

“It would not be absurd to imagine a universe where, after the example of our solar system, the total internal energy might go on diminishing while the fraction remaining would constantly pass into an unusable form, where energy would be lost and at the same time degraded.

“The law of the conservation of energy is only a definition: the proof of this is that when a new phenomenon comes to establish a discord in the equation of energy, there is set up for it a new form of energy defined by the conditions of reestablishing the compromised inequality”.

And in answer to a letter in which I set forth my ideas on this point, the same physicist wrote to me: —

“The ‘nothing is lost’ should be deleted from the exposition of the laws of physics, for the science of today teaches us that something is lost. It is certainly in the direction of the leakage, of the wearing away of the worlds, and not in the direction of their greater stability, that the science of tomorrow will modify the reigning ideas”.

I have faithfully set forth, in this and the preceding chapters, the theories which rule science at present. My criticisms have not interfered with the faithfulness of my exposition. Their object was simply to show that the current theories contain some very weak points, and that consequently it is permissible to replace them, or at least to prepare for their replacement. No longer fettered by the weight of early principles now sufficiently shaken, we can proceed to examine whether, in place of being indestructible, energy does not vanish without return, like that matter of which it is only the transformation.

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