CHAPTER I.

ENERGY IN GENERAL.

Origin of the Idea of Energy.—The Phenomena of Nature bring into play only two Elements, Matter and Energy.—§ 1. Matter.—§ 2. Energy.—§ 3. Mechanical Energy.—§ 4. Thermal Energy.—§ 5. Chemical Energy.—§ 6. The Transformations of Energy.—§ 7. The Principles of Energetics.—The Principle of the Conservation of Energy.—§ 8. Carnot’s Principle.—The Degradation of Energy.

_Origin of the Idea of Energy._—A new term, namely _energy_, has been for some years introduced into natural science, and has ever since assumed a more and more important place. It is owing to the English physicists, and especially to the English electrical engineers, that this expression has made its way into technology, an expression which is part and parcel of both languages, and which has the same meaning in both. The idea it expresses is, in fact, of infinite value in industrial applications, and that is why its use has gradually spread and become generalized. But it is not merely a practical idea. It is above all a theoretical idea of capital importance to pure theory. It has become the point of departure of a science, _energetics_, which, although born but yesterday, already claims to embrace, co-ordinate, and blend within itself all the other sciences of physical and living nature, which the imperfection of our knowledge alone had hitherto kept distinct and apart.

On the threshold of this new science we find inscribed _the principle of the conservation of energy_, which has been presented to us by some as Nature’s supreme law, and which we may say dominates natural philosophy. Its discovery marked a new era and accomplished a profound revolution in our conception of the universe. It is due to a doctor, Robert Mayer, who practised in a little town in Wurtemberg, and who formulated the new principle in 1842, and afterwards developed its consequences in a series of publications between 1845 and 1851. They remained almost unknown until Helmholtz, in his celebrated memoir on the conservation of force, brought them to light and gave them the importance they deserved. From that time forward the name of the doctor of Heilbronn, until then obscure, has taken its place among the most honoured names in the history of science.[5]

[5] Mayer’s claim to fame has been disputed. A Scotch physicist, P. G. Tait, has investigated the history of the law of the conservation of energy, which is the history of the idea of energy. The conception has taken time to penetrate the human mind, but its experimental proof is of recent date. P. G. Tait finds an almost complete expression of the law of the conservation of energy in Newton’s third law of motion—namely, “the law of the equality of action and reaction,” or rather, in the second explanation which Newton gave of that law. In fact, it was from this law that Helmholtz deduced it in 1847. He showed that the law of the equality of action and reaction, considered as a law of nature, involved the impossibility of perpetual motion, and the impossibility of perpetual motion is, in another form, the conservation of energy.

At a meeting of the Academy of Science, at Berlin, 28th March 1878, Du Bois-Reymond violently attacked Tait’s contention. The honour of having been the first to conceive of the idea of energy and conservation was awarded to Leibniz. Newton had no right to it, for he appealed to divine intervention to set the planetary system on its path when disturbed by accumulated perturbations. On the other hand, Colding claims to have drawn his knowledge of the law of conservation from d’Alembert’s principle. Whatever may be the theoretical foundations of this law, we are here dealing with its experimental proof. According to Tait, the proof can no more be attributed to R. Mayer than to Seguin. The real modern authors of the principle of the conservation of energy, who gave an experimental proof of it, are Colding, of Copenhagen, and Joule, of Manchester.

As for _energetics_, of which thermodynamics is only a section, it is agreed that even if it cannot forthwith absorb mechanics, astronomy, physics, chemistry, and physiology, and build up that general science which will be in the future the one and only science of nature, it furnishes a preparation for that ideal state, and is a first step in the ascent to definite progress.

Here I propose to expound these new ideas, in so far as they contain anything universally accessible; and in the second place, I propose to show their application to physiology—that is to say, to point out their rôle and their influence in the phenomena of life.

_Postulate: the Phenomena of Nature bring into play only two Elements, Matter and Energy._—If we try to account for the phenomena of the universe, we must admit with most physicists that they bring into play two elements, and two elements only; namely, _matter_ and _energy_. All manifestations are exhibited in one or other of these two forms. This, we may say, is the postulate of experimental science.

Just as gold, lead, oxygen, the metalloids, and the metals are different kinds of matter, so it has been recognized that sound, light, heat, and generally, the imponderable agents of the days of early physics, are different varieties of energy. The first of these ideas is older and more familiar to us, but it has not for that reason a more certain existence. Energy is objective reality for the same reason that matter is. The latter certainly appears more tangible and more easily grasped by the senses. But, upon reflection, we are assured that the best proof of their existence, in both cases, is given by the law of their conservation—that is to say, their persistence in subsisting.

The objective existence of matter and that of energy will therefore be taken here as a postulate of physical science. Metaphysicians may discuss them. We have but little room for such a discussion.

§ I. MATTER.

It is certainly difficult to give a definition of matter which will satisfy both physicists and metaphysicians.

_Mechanical Explanation of the Universe. Matter is Mass._—Physicists have a tendency to consider all natural phenomena from the point of view of mechanics. They believe that there is a mechanical explanation of the universe. They are always on the look out for it, implicitly or explicitly. They endeavour to reduce each category of physical facts to the type of the facts of mechanics. They have made up their minds to see nowhere anything but the play of motion and force. Astronomy is celestial mechanics. Acoustics is the mechanics of the vibratory movements of the air or of sonorous bodies. Physical optics has become the mechanics of the undulations of the ether, after having been the mechanics of emission—a wonderful mechanics which represents exactly all the phenomena of light, and furnishes us with a perfect objective image of it. Heat, in its turn, has been reduced to a mode of motion, and thermodynamics claims to embrace all its manifestations. As early as 1812, Sir Humphry Davy wrote as follows:—“The immediate cause of heat is motion, and the laws of transmission are precisely the same as those of the transmission of motion.” From that time forth, this conception developed into what is really a science. The constitution of gases has been conceived by means of two elements—particles, and the motions of these particles, determined in the strictest detail. And finally, in spite of the difficulties of the representation of electrical and magnetic phenomena after Ampère and before Maxwell and Hertz, physicists have been able to announce in the second half of the nineteenth century the unity of the physical forces realized in and by mechanics. From that time forth, all phenomena have been conceived as motion or modes of motion, only differing essentially one from the other in so far as motions may differ—that is to say, in the masses of the moving particles, their velocities, and their trajectories. The external world has appeared essentially homogeneous; it has fallen a prize to mechanics. Above all, there is heterogeneity in ourselves. It is in the brain, which responds to the nervous influx engendered by the longitudinal vibration of the air, by the specific sensation of sound, which responds to the transverse vibration of the ether by a luminous sensation, and in general to each form of motion by an irreducible specific sensation.

Forty years have passed since the mechanical explanation of the universe reached its definite and perfect form. It dominates physics under the name of the _theory of kinetic energy_. The minds of men in our own time are so strongly impregnated with this idea that most scientists of ordinary culture get no glimpse of the world of phenomena but by means of this conception. And yet it is only an hypothesis. But it is so simple, so intuitive, and appears to be so thoroughly verified by experiment, that we have ceased to recognize its arbitrary and unnecessarily contingent character. Many physicists from this standpoint consider the kinetic theory as an imperishable monument.

However, as in the case of H. Poincaré, the most eminent physicists and mathematicians are not the dupes of this system; and without failing to recognize the immense services which it has rendered to science, they are perfectly well aware that it is only a system, and that there may be other systems. Certain among them, such as Ostwald, Mach, and Duhem, believe that the monument is showing signs of decay, and at present the theory is opposed by another theory—namely, the theory of _energy_.

The theory of _energy_ is usually considered and presented as a consequence of the kinetic theory; but it is perfectly independent of it, and it is, in fact, without relying on the kinetic theory, without assuming the unity of physical forces, which are combined in molecular mechanics, that we shall expound the general system.

This is not the point at issue for the moment. It is not a question of deciding the reality or the merit of this or that mechanical explanation; it is a question of something more general, because upon it depends the _idea of matter_. It is a question of knowing if there are any explanations other than mechanical. The illustrious English physicist, Lord Kelvin, does not seem willing to admit this. “I am never satisfied,” he said, in his _Molecular Mechanics_, “until I have made a mechanical model of the object. If I can make this model, I understand; if I cannot, I do not understand.”

This tendency of so vigorous a mind to be content only with mechanical explanations, has been that of the majority of scientific men up to the present day, and from it has arisen the scientific idea of matter.

What is matter, in fact, to the student of mechanics? It is mass. All mechanics is constructed of masses and forces. Laplace said: “The mass of a body is the sum of its material points.” To Poisson, mass is the quantity of matter of which a body is composed. Matter is therefore confused with mass. Now, mass is the characteristic of the motion of a body under the action of a given force; it defines obedience or resistance to the causes of motion; it is the _mechanical parameter_; it is the co-efficient proper to every mobile body; it is the first _invariant_ of which a conception has been established by science.

In fact, the word matter appears to be used in other senses by physicists, but this is only apparently so. They have but broadened the idea of the mechanicians. They have characterized matter by the whole series of phenomenal manifestations which are _proportional to mass_, such as weight, volume, chemical properties—so that we may say that the notion of matter does not intervene scientifically with a different signification from that of mass.

_Two kinds of Matter. Ponderable and Imponderable._—In physics we distinguish between two kinds of matter—ponderable, obeying the law of universal attraction or weight, and imponderable matter or ether, which we assume to exist and to escape the action of that force. Ether has no weight, or extremely little weight. It is material in so far as it has mass. It is its mass which confers existence on it from the mechanical point of view—a logical existence, inferred from the necessity of explaining the propagation of heat, light, or electricity.

It may be observed that the use of mass really comes to bringing another element, force, to intervene, and we shall see that force is connected with energy; thus it comes to defining matter indirectly by energy. The two fundamental elements are not therefore irreducible; on the contrary, they should be one and the same thing.

_Energy is the only Objective Reality._—This fusion into one will become more evident still when we examine the different kinds of energy, each of which exactly corresponds to one of the aspects of active matter. Shall we define matter by _extension_, by the portion of space it occupies, as certain philosophers do? The physicist will answer that space is only known to us by the expenditure of energy necessary to penetrate it (the activity of our different senses). And then what is weight? It is _energy of position_ (universal attraction). And so with the other attributes. So that if matter were separated from the energetic phenomena by means of which it is revealed to us—weight or energy of position, impenetrability or energy of volume, chemical properties or chemical energies, mass or capacity for kinetic energy—the very idea of matter would vanish. And that comes to saying that fundamentally there is only one objective reality, _energy_.

_Philosophical Point of View._—But from the philosophical point of view are there objective realities? That is a wider question which throws doubt upon matter itself, and which it is not our place to investigate here. A metaphysician may always discuss and deny the existence of the objective world. It may be maintained that man knows nothing beyond his sensations, and that he only objectivates them and projects them outside himself by a kind of hereditary illusion. We must avoid taking sides in all these difficulties. Physics for the moment ignores them—_i.e._, postpones their consideration.

In a first approximation we agree to consider ponderable matter only. Chemistry acquaints us with its different forms. They are the different simple bodies, metalloids, metals, and the compound bodies, mineral or organic. Hence we may say that chemistry is _the history of the transformations of matter_. From the time of Lavoisier this science has followed the transformations of matter, balance in hand, and ascertains that they are accomplished without change of weight.

_Law of the Conservation of Matter._—Imagine a system of bodies enclosed in a closed vessel, and the vessel placed in the scale of a balance. All the chemical reactions capable of completely modifying the state of this system have no effect upon the scale of the balance. The total weight is the same before, during, and after. It is precisely this equality of weight which is expressed in all the equations with which treatises on chemistry are filled.

From a higher point of view we recognize here, in this _law of Lavoisier_ or of the _conservation of weight_, the verification of one of the great laws of nature which we extend to every kind of matter, ponderable or not. It is the _law of the conservation of matter_, or again, of the indestructibility of matter—“Nothing is lost, nothing is created, all is transformation.” This is exactly what Tait held, this impossibility of creating or destroying matter which at the same time is a proof of its objective existence. This indestructibility of ponderable matter is at the same time the fundamental basis of chemistry. Chemical analysis could not exist if the chemist were not sure that the contents of his vessel at the end of his operations ought to be quantitatively, that is to say by weight, the same as at the beginning, and during the whole course of the experiment.[6]

[6] It must be added that the absolute rigour of this law has been called in question in recent researches. It would only have an approximate value.

§ 2. ENERGY.

_The Idea of Energy Derived from the Kinetic Theory._—The notion of energy is not less clear than the notion of matter, it is only more novel to our minds. We are led to it by the mechanical conception which now dominates the whole of physics, _the kinetic conception_, according to which in the sensible universe there are no phenomena but those of motion. Heat, sound, light, with all their manifestations so complex and so varied, may, according to this theory, be explained by motion. But then, if outside the brain and the mind which has consciousness and which perceives, Nature really offers us only motion, it follows that all phenomena are essentially homogenous among one another, and that their apparent heterogeneity is only the result of the intervention of our sensorium. They differ only in so far as movements are capable of differing—that is to say, in velocity, mass, and trajectory. There is something fundamental which is common to them and this _quid commune_ is _energy_. Thus the idea of energy may be derived from the kinetic conception, and this is the usual method of exposition.

This method has the great inconvenience of causing an idea which lays claim to reality to depend upon an hypothesis. And besides that, it gives a view of it which may be false. It makes of the different forms of energy something more than varieties which are equivalent to one another. It makes of them _one and the same thing_. It blends into one the modalities of energy and mechanical energy. For the experimental idea of equivalence, the kinetic theory substitutes the arbitrary idea of the equality, the blending, and the fundamental homogeneity of phenomena. This no doubt is how the founders of energetics, Helmholtz, Clausius, and Lord Kelvin understood things. But a more attentive study and a more scrupulous determination not to go beyond the teaching of experiment should compel us to reform this manner of looking at it. And it is Ostwald’s merit that, after Hamilton, he insisted on this truth—that the various kinds of physical magnitudes furnished by the observation of phenomena are different and characteristic. In particular, we may distinguish among them those which belong to the order of _scalar_ magnitudes and others which are of the order of _vector_ magnitudes.

_The Idea of Energy derived from the Connection of Phenomena._—The idea of energy is not absolutely connected with the kinetic theory, and it should not be exposed therefore to the vicissitudes experienced by that theory. It is of a higher order of truth. We can derive it from a less unsafe idea, namely that of the _connection of natural phenomena_. To conceive it we must get accustomed to this primordial truth, that there are no _phenomena isolated_ in time and space. This statement contains the whole point of view of energetics.

The physics of early days had only an incomplete view of things, for it considered phenomena independently the one of the other.

Phenomena for purposes of analysis were classed in separate and distinct compartments: weight, heat, electricity, magnetism, light. Each phenomenon was studied without reference to that it succeeded or that which should follow. Nothing could be more artificial than such a method as this. In fact, there is a sequence in everything, everything is connected up, _everything precedes and succeeds in nature_—in nature there are only series. The isolated fact without antecedent or consequent is a myth. Each phenomenal manifestation is in solidarity with another. It is a metamorphosis of one state of things into another. It is transformation. It implies a state of things anterior to that which we are observing, a phenomenal form which has preceded the form of the present moment.

Now there exists a link between the anterior state and the succeeding state—that is to say, between the new form which is appearing and the preceding form which is disappearing. The science of energy shows that something has passed from the first condition to the second, but covering itself as it were with a new garment; in a word, that something active and permanent subsists in the passage from one condition to another, and that what has changed is only the aspect, the appearance.

This constant something which is perceived beneath the inconstancy and the variety of forms, and which circulates in a certain manner from the antecedent phenomenon to its successor, is energy.

But still this is only a very vague view, and it may seem arbitrary. It may be made more exact by examples borrowed from the different categories of natural phenomena. There are energetic modalities in relation with the different phenomenal modalities. The different orders of phenomena which may be presented—mechanical, chemical, thermal, electrical—give rise to corresponding forms of energy.

When to a mechanical phenomenon succeeds a mechanical, thermal, or electrical phenomenon, we say, embracing transformation in its totality, that there has been a transformation of mechanical energy into another form of energy, mechanical, thermal, or electrical, etc.

This idea becomes more precise if we examine successively each of these cases and the laws which regulate them.

§ 3. MECHANICAL ENERGY.

Mechanical energy is the simplest and the oldest known.

_Mechanical Elements: Time, Space, Force, Work, Power._—Mechanical phenomena may be considered under two fundamental conditions—_time_ and _space_, which are, in a measure, logical elements, to which may be joined a third element, itself experimental, having its foundations in our sensations—namely, _force_, _work_, or _power_.

The ideas of force, work, and power, are drawn from the experience man has of his muscular activity. Nevertheless the greatest mathematical minds from from Descartes to Leibniz have been obliged to define and explain them clearly.

_Force_.—The prototype of force is weight, universal attraction. Experiment shows us that every body falls as long as no obstacle opposes its fall. This is so universal a property of matter that it serves to define it. The _force_, weight, is therefore the name given to the cause of the fall of the bodies.

Force in general is the _cause of motion_. Hence force exists only in so far as there is motion. There would be no force without action. This is Newton’s point of view. It did not prevail, and was not the point of view of his successors. The name of force has been given not only to the cause which produces or modifies motion, but to the cause which resists and prevents it. And then not only have _forces in action_ been considered (dynamics), but _forces at rest_ (statics). Now, to Newton there was no statics. Forces do not continue to exist when they produce no motion; they are not in equilibrium, they are destroyed.

The idea of force therefore is a metaphysical idea which contains the idea of _cause_. But it becomes experimental immediately it is looked upon as resisting motion, according to the point of view of Newton’s opponents. Its foundations lie in the muscular activity of man.

Man can support a burden without bending or moving. This burden is a weight—that is to say, a mass acted on by the force of weight. Man resists this force so as to prevent its effect. If it were not annihilated by man’s _effort_, this effect would be the motion or the fall of the heavy body. The _effort_ and the force are thus in equilibrium, and the effort is equal and opposite to the force. It gives to the man who exercises it the conscious idea of _force_. Thus we know of force through effort. Every clear idea that we can have of _force_ springs from the observation of our muscular effort.

The notion of force is thus an anthropomorphic notion. When an effect is produced in nature outside human intervention, we say that it is by something analogous to what in man is effort, and we give to this something a name which is also analogous, namely _force_. To give a name to _effort_ and to compare efforts in magnitude, we need not know all about them, nor need we know in what they essentially consist, of what series of physical, chemical, and physiological actions they are the consequence. And so it is with force. It is a resistance to motion or the cause of motion. This cause of motion may be an anterior motion (kinetic force). It may be an anterior physical energy (physical and chemical forces).

Forces are measured in the C.G.S. system by comparing them with the unit called the Dyne.[7] In practice they are compared with a much larger unit—the gramme, which is the weight, the force acting on a unit of mass of one centimetre of distilled water at a temperature of 4° C.

[7] The dyne is the force which applied to the unit of mass produces a unit of acceleration.

_Work._—The muscular activity of man may be brought into play in yet another manner. When we employ workmen, as Carnot said in his _Essai sur l’équilibre et le mouvement_, it is not a question of “knowing the burdens that they can carry without moving from their position,” but rather the burdens that they can carry from one point to another. For instance, a workman may have to lift the water from the bottom of a well to a given height, and the case is the same for the animals we employ. “This is what we understand by force when we say that the force of a horse is equal to the force of seven men. We do not mean that if seven men were pulling in one direction and the horse in another that there would be equilibrium, but that in a piece of work the horse alone would lift, for example, as much water from the bottom of a well to a given height as the seven men together would do in the same time.”[8]

[8] These words spoil the statement, for time has nothing to do with it.

Here, then, we have to do with the second form of muscular activity, which is called in mechanics, “work”—at least, if in the preceding quotation we attach no particular importance to the words “in the same time,” and retain the employment of muscular activity only “under constant conditions.” Mechanical work is compared with the elevation of a certain weight to a certain height. It is measured by the product of the force (understood in the sense in which it was used just now—that is to say, as causing or resisting motion) and the displacement due to this motion. The unit is the Kilogrammetre—that is to say, the work necessary to lift a weight of one kilogramme to the height of one metre.

It will be remarked that the idea of time does not intervene in our estimation of work. The notion of work is independent of the ideas of velocity and time. “The greater or less time that we take to do a piece of work is of no more assistance in measuring its magnitude than the number of years that a man may have taken to grow rich or to ruin himself can help to estimate the present amount of his fortune.”

Going back to Carnot’s comparison, an employer who employed his workmen only on piece-work,—that is to say, who would only care about the amount of work done, and would be indifferent to the time that they took over it,—would be at the same point of view as the advocates of the mechanical theory. M. Bouasse, whom we follow here, has remarked that this idea of mechanical work may be traced back to Descartes. His predecessors, and Galileo in particular, had quite a different idea of the way in which mechanical activity should be measured; and so, among the mathematicians of the eighteenth century, Leibniz and, later, John Bernoulli were almost alone in looking at it from this point of view.

_Energy._—Work thus understood is _mechanical energy_. It represents the lasting and objective effect of the mechanical activity independent of all the circumstances under which it was carried out. The same work may be done under very different conditions of time, velocity, force, and displacement. It is therefore the permanent element in the variety of mechanical aspects. Work, for example, in the collision of bodies when the motion of a body appears to be destroyed on impact with another, reappears as indestructible _vis viva_. This, then, is exactly what we call _energy_; and if we agree to give it this name, we may say that the conservation of energy is invariable throughout all mechanical transformations.

_Distinction between Work and Force, and between Energy and Work._—The history of mechanics shows us what trouble has been taken and what efforts have been made to distinguish work (now mechanical energy) from force.

It is worth while insisting on this distinction. It could be easily shown that force has no objective existence. It has no duration, no permanence. It does not survive its effect, motion. There is no conservation of force. It passes instantly from infinity to zero. It is a _vectorial magnitude_—that is to say, it involves the idea of direction. Work, on the other hand, is the real element; it is a _scalar magnitude_ involving the idea of opposite directions, indicated by the signs + and-. Work and force are heterogeneous magnitudes. Energy, and this is the only characteristic by which it is distinguished from work, is an _absolute magnitude_ to which we may not even give opposite signs.

An example may perhaps throw these characteristics into relief—namely, the hydraulic press. We have on the platform exactly the work which has been done on the other side. The machine has only made it change its form. On the contrary, the force has been infinitely multiplied. We may, in fact, consider an infinite number of surfaces equal to that of a small piston, placed and orientated at will within the liquid; each, according to Pascal’s principle, will support a pressure equal to that which is exercised. As soon as we cease to support it, this infinity falls at once to zero. Now what real thing could pass instantly from infinity to zero?

That skilful and very able physiologist, M. Chauveau, has endeavoured to use the same term _energy of contraction_ for the two phenomena of effort (force) and work. It seems, however, from the point of view of the expenditure imposed on the organism, that these two modes of activity, _static contraction_ (effort), and _dynamical contraction_ (work), may be, in fact, perfectly comparable. But although this manner of conceiving the phenomena may certainly be exact, and may be of great value, the idea of force must none the less remain distinct from that of work. The persistence of the author in violating established custom in this connection has prevented him from enabling mechanicians and even some physiologists to understand and accept very useful truths.

_Power._—The idea of mechanical _power_ differs from those of force and work. The idea of time must intervene. It is not sufficient, in fact, in order to characterize a mechanical operation, to point to the task accomplished. It may be necessary or useful to know how much time it required. This is true, especially when we are concerned with the circumstances as well as the results of the performance of the work; and this is the case when we wish to compare machines. We say that the machine which does the work in the shortest space of time is the most powerful. The unit of power is the Kilogrammetre-second—that is to say, the power of a machine which does a kilogrammetre in a second. In manufactures we generally employ a unit 75 times greater than this—a _horse-power_. This is the power of a machine which does 75 kilogrammetres a second. In the electrical industry we measure by _kilowatts_, which are equivalent to 1.36 horse power, or by a _watt_, a unit a thousand times smaller.

Let us add that the power of a machine is not an absolute and permanent characteristic of the machine. It depends on the circumstances under which the work is carried out, and that is why, in particular, we cannot appreciate the power of the human machine in comparison with industrial machines. Experience has shown that the mechanical power of living beings depends upon the nature of the work they are doing. In this connection we may mention some very interesting experiments communicated to the Institute, in the year VI., by the celebrated physicist, Coulomb. A man of the average weight of 70 kilogrammes was made to climb the stairs of a house 20 metres high. He ascended at the rate of 14 metres a minute, and he performed this daily task for four effective hours. This work was equivalent to 235,000 kilogrammetres. But if, instead of climbing without a burden, the same man had had to carry a load, the result would have been quite different. Coulomb’s workman took up six loads of wood a day to a height of 12 metres in 66 journeys, corresponding to a maximum work of 109,000 instead of 235,000 kilogrammetres. The mechanical power of the human machine thus varied in the two cases in the ratio of 235 to 109.

_The Two Aspects of Mechanical Energy: Kinetic and Potential._—Energy, or mechanical work, may present itself in two forms—kinetic energy, corresponding to the mechanical phenomenon which has really taken place, and _potential energy_, or the energy of reserve.

A body which has been raised to a certain height will, if it be let fall, perform work which can be exactly measured in kilogrammetres by the product of its weight into the height it falls. Such work may be utilized in many ways. In this way, for instance, public clocks are worked. Now, as long as the clock-weight is raised and not let go, and as long as it is motionless, the physics of early days would say that there is nothing to discuss; the phenomenon is the fall; it is going to take place, but at the present moment there has been no fall.

In energetics we do not reason in this way. We say that the body possesses a _capacity for work_ which will be manifested when the opportunity arises, a storage of energy, a virtual or _potential energy_, or again, an _energy of position_, which will be transformed into actual energy or real work as soon as the body falls.

Let us ask whence this energy arises. It proceeds from the previous operation which has raised the weight from the surface of the soil to the position it occupies. For example, if it is a question of the weights of a public clock, which, by its fall, will develop in 15 days the work that is necessary to turn the wheels, to strike the bell, and to turn the hands, this work ought to bring to our minds the exactly equal and opposite work done by the clockmaker, who has to carry the clock-weight and to lift it up from the ground to its point of departure. The work of the fall is the faithful counterpart of the work of elevation. The phenomenon has therefore in reality two phases. We find in the second exactly what was put into the first, the same quantity of energy—_i.e._, the same work. Between these phases comes the intermediary phase of which we say that it is a period of virtual _or potential energy_. This is a way of remembering in some measure the preceding phenomenon—_i.e._, the work of lifting up, and of indicating the phenomena which will follow—_i.e._, the work of the fall. And thus we connect by our thoughts the present situation with the antecedent and with the consequent position, and it is from this consideration of continuity alone that the conception of energy springs—that is to say, of something which is conserved and is found to be permanent in the succession of phenomena. This energy of which we lose no trace does not appear to us new when it is manifested. Our imagination eventually materializes the idea of it. We follow it as a real thing, having an objective existence, which is asleep during the latent potential period, and is revealed or manifested later.

Among other examples, that of the coiled spring which is unwound is particularly suitable for showing this fundamental character of the idea of mechanical energy, an idea which is the clearest of all. Machines are only transformers and not creators of mechanical energy. They only change one form into another.

In the same way, too, a stream of water or the torrent of a mountainous region may be utilized for setting in motion the wheels and the turbines of the factories situated in the valley. Its descent produces the mechanical work which would be a creation _ex nihilo_ if we do not connect the phenomenon with its antecedents. We look on it as a simple restitution, if we think of the origin of this water which has been transported and lifted in some way to its level by the play of natural forces—evaporation under the action of the sun, the formation of clouds, transport by winds, etc. And we here again see that a complex energy has been transformed, in its first phenomenal condition, into _potential energy_, and that this potential energy is always expended in the second phase without loss or gain.

_The Different Kinds of Mechanical Energy; of Motion, of Position._—There are as many forms of energy as there are distinct categories of phenomena or of varieties in these categories. Physicists distinguish between two kinds of mechanical energy—energy of motion and energy of position. The energy of position presents several variants—energy of distance, which corresponds to force: of this we have just spoken; energy of surface, which corresponds to particular phenomena of surface tension; and energy of volume which corresponds to the phenomena of pressure. Energy of motion, _kinetic energy_, is measured in two ways: as work (the product of force and displacement, W = _fs_) or as _vis viva_ (half the product of the mass into the square of the velocity U = _mv^2_∕2.)[9]

[9] We therefore notice that the measures of force and work bring in mass, space, and time. The typical force, weight, is given by w = mg. On the other hand, we have by the laws of falling bodies _v_ = _gt_; _s_ = 1∕2_gt^2_; whence _g_ = 2_s_∕_t^2_; _w_ = _m_(2_s_∕_t^2_); or, if F be the force, M the mass, L the space described, and T the time, we have F = MLT^{-2}, which expresses what are called the dimensions of the force—that is to say, the magnitudes with their degree, which enter into its expression. We may thus easily obtain the dimensions of work:—

_Work_ = _f_ × _s_ = _mv^2_∕2 = ML^2T^{-2}.

§ 4. THERMAL ENERGY.

In the elements of physics it is nowadays taught that mechanical work may be transformed into heat, and reciprocally that heat may be transformed into mechanical work. Friction, impact, pressure, and expansion destroy or annihilate the mechanical energy communicated to a body or to the organs of a machine. With the disappearance of motion we note the appearance of heat. Examples abound. The tyre of a wheel is heated by the friction of the road. Portions of steel are warmed by the impact with stone, as in the old flint and steel. Two pieces of ice were melted by Davy, who rubbed them one against the other, the external temperature being below zero. The boiling of a mass of water caused by a drill was noticed by Rumford in 1790, during the manufacture of bronze cannon. Metal, beaten on an anvil, is heated. A leaden ball flattened against a resisting obstacle shows increase of temperature carried to the point of fusion. Finally, and symbolically, we have the origin of fire in the fable of Prometheus, by rubbing together the pieces of wood which the Hindoos called _pramantha_. Correlation is constant between the thermal and mechanical phenomena, a correlation that becomes evident as soon as observers have ceased to restrict themselves to the determination in isolation of the one fact or the other. There is never any real destruction of heat and motion in the true sense of the word; what disappears in one form appears again in another; just as if something indestructible were appearing in a series of successive disguises. This impression is translated into words when we speak of the metamorphosis of mechanical into thermal energy.

_The Mechanical Equivalent of Heat._—The interpretation assumes a remarkable character of precision, which at once strikes the mind when physics applies to these transformations the almost absolute accuracy of its measurements. We then find that the rate of exchange is invariable. Transformations of heat into motion, and of motion into heat, take place according to a rigorous numerical law, which brings into exact correspondence the quantity of each. Mechanical effect is estimated, as we have seen, by work, that is in kilogrammetres. Heat is measured in calories, the calorie being the quantity of heat necessary to raise from 0°C to 1°C a kilogramme of water (Calorie) or one gramme of water (calorie). It is found that whatever may be the bodies and the phenomena which serve as intermediaries for carrying out this transformation, we must always expend 425 kilogrammetres to create a Calorie, or expend 0·00234 Calories to create a kilogrammetre. The number 425 is the mechanical equivalent of the Calorie, or, as is incorrectly stated, of the heat. It is this constant fact which constitutes _the principle of the equivalence of heat and of mechanical work_.

§ 5. CHEMICAL ENERGY.

We cannot yet actually measure chemical activity directly, but we know that chemical action may give rise to all other phenomenal modalities. It is their most ordinary source, and it is to it that industries appeal to obtain heat, electricity, and mechanical action. In the steam engine, for instance, the work that is received arises from the combustion of carbon by the oxygen of the air. This gives rise to the heat which vaporizes the water, produces the tension of the steam, and ultimately produces the displacement of the piston. The theory of the steam engine might be reduced to these two propositions: chemical activity gives rise to heat, and heat gives rise to motion; or to use the language to which the reader by now will be accustomed, chemical energy is transformed into thermal energy, and that into mechanical energy. It is a series of phases and of instantaneous changes, and the exchange is always affected according to a fixed rate.

_The Measurement of Chemical Energy._—Our knowledge of chemical energy is less advanced than that of the energies of heat and sensible motion. We have not yet reached the stage of numerical verifications. We can only therefore affirm the equivalence of chemical and thermal energies without the aid of numerical constants, because we do not yet, in the present state of science, know how to measure chemical energy directly. Other known energies are always the product of two factors: the mechanical energy of position, or work, is measured by the product of the force _f_, and the displacement _s_; work = _fs_; the mechanical energy of motion, U = 1∕2_mv^2_, is measured by the product of the mass into half the square of the velocity. Thermal energy is measured by the product of the temperature and the specific heat; electric energy by the product of the quantity of electricity (in coulombs) and of the electromotive force (in volts). As for chemical energy, we guess that it may be valued directly according to Berthollet’s system, adopted by the Norwegian chemists, Guldberg and Waage, by means of the product of the masses and of a force, or co-efficient of affinity, which depends on the nature of the substances which are brought together, on the temperature, and on the other physical circumstances of the reaction. On the other hand, the researches of M. Berthelot enable us in many cases to obtain an indirect valuation in terms of the equivalent heat.

_Its Two Forms._—It is interesting to note that chemical energy may also be regarded from the two states of _potential_ and _kinetic energy_. The coal-oxygen system, to burn in the furnace of the steam engine, must be primed by preliminary work (local ignition), just as the weight that is raised and left motionless at a certain height requires a small effort to be detached from its support. When this condition is fulfilled, energy is at once manifest. We must admit that it existed in the latent state, in the state of _chemical potential energy_. Under the impulse received, the carbon combines with the oxygen and forms carbonic acid, C + 2O becomes CO⌄{2}; potential energy is changed into actual chemical energy, and immediately afterwards into thermal energy. We should have only a very incomplete and fragmentary view of the reality of things if we were to consider this phenomenon of combustion in isolation. We must consider it in connection with what has actually created the energy which it is about to dissipate. This antecedent fact is the action of the sun upon the green leaf. The carbon which burns in the furnace of the machine comes from the mine in which it was stored in the form of coal—that is to say, of a product which was vegetable in its primitive form, and which was formed at the expense of the carbonic acid of the air. The plant had separated, at the expense of the solar energy, the carbon from the oxygen to which it was united in the carbonic acid of the atmosphere. It had created the system C + 2O. So that the solar energy produces the chemical potential energy which was so long before it was utilized. Combustion expends this energy in making carbonic acid over again.

_Materialization of Energy._—The fertility of the idea of energy is therefore, as we see from all these examples, due to the relations it establishes between the natural phenomena of which it exhibits the necessary relation, destroyed by the excessive analysis of early science. It shows us that in the world of phenomena there is nothing but transformations of energy. And we regard these transformations themselves as the circulation of a kind of indestructible agent which passes from one form of determination to another, as if it were simply putting on a fresh disguise. If our intellect requires images or symbols to embrace the facts and to grasp their relation, it may introduce them here. It will materialize energy, it will make of it a kind of imaginary being, and confer upon it an objective reality. And for the mind, as long as it does not become the dupe of the phantom which it itself has created, this is an eminently comprehensive artifice which enables us to grasp readily the relations between phenomena and their bond of affiliation.

The world appears to us then, as we said at the outset, constructed with singular symmetry. It offers to us nothing but transformations of matter and transformations of energy; these two kinds of metamorphoses being governed by two laws equally inevitable, the conservation of matter and the conservation of energy. The first of these laws expresses the fact that matter is indestructible, and passes from one phenomenal determination to another at a rate of equivalence measured by weight; the second, that energy is indestructible, and that it passes from one phenomenal determination to another at a rate of equivalence fixed for each category by the discoveries of the physicists.

§ 6. TRANSFORMATIONS OF ENERGY.

The idea of energy has become the point of departure of a science, _Energetics_, to the establishment of which a large number of contemporary physicists, among whom are Ostwald, Le Châtelier, etc., have devoted their efforts. It is the study of phenomena, regarded from the point of view of _energy_. I have said that it claims to co-ordinate and to embrace all other sciences.

The first object of energetics should be the consideration of the different forms of energy at present known, their definition and their measurement. This is what we have just done in broad outline.

In the second place, each form of energy must be regarded with reference to the rest, so as to determine if the transformation of this into that is directly realizable, and by what means, and, finally, according to what rate of equivalence. This new chapter is a laborious task which would compel us to traverse the whole field of physics.

Of this long examination we need only concern ourselves here with three or four results which will be more particularly important in the case of applications to living beings. They refer to mechanical energy, to the relations of thermal energy and chemical energy, to the complete rôle of thermal energy, and finally to the extreme adaptability of electrical energy.

1. _Transformation of Mechanical Energy._—Mechanical energy may change into every other form of energy, and all others can change into it, with but one exception, that of chemical energy. Mechanical effort does not produce chemical combination. What we know of the part played by pressure in the reactions of dissociation seems at first to contradict this assertion. But this is only in appearance. Pressure intervenes in these operations only as _preliminary work_ or _priming_, the purpose of which is to bring the bodies into contact in the exact state in which they must be for the chemical affinities to be able to enter into play.

2. _Transformation of Thermal Energy; Priming._—Thermal (or luminous) energy does not change directly into chemical energy. In fact, heat and light favour and even determine a large number of chemical reactions; but if we go down to the foundation of things we are not long before we feel assured that heat and light only serve in some measure for _priming_ for the phenomenon, for preparing the chemical action, for bringing the body into the physical state (liquid, steam) or to the degree of temperature (400° C. for instance, for the combination of oxygen and hydrogen) which are the preliminary indispensable conditions for the entry upon the scene of chemical affinities.

On the contrary, chemical energy may really be transformed into thermal energy. We have an instance of this in the reactions which take place without the aid of external energy; and again, in those very numerous cases which, such as the combustion of hydrogen and carbon, or the decomposition of explosives, the reactions continue when once primed. I may make a further observation apropos of thermal and photic energy. These are not two really and essentially distinct forms, as was thought in the early days of physics. When we consider things objectively, there is absolutely no light without heat; light and heat are one and the same agent. According as it is at this or that degree of its scale of magnitude, it makes a stronger impression on the skin (sensation of heat) or on the retina (sensation of light) of man and animals. The difference may be put down to the diversity of the work and not to that of the agent. The kinetic theory shows us that the agent is qualitatively identical. The words heat and light only express the chance of the meeting of the radiant agent with a skin and a retina. At the lowest degree of activity this agent exerts no action on the terminations of the thermal cutaneous nerves, nor on the optic nerve-terminations. As this degree is raised the former of these nerves are affected (cold, heat) and are so to the exclusion of the nerves of vision. Then they are both affected (sensation of heat and light), and finally, beyond that, sight alone is affected. The transformation of one energy into the other is therefore here reduced to the possibility of increasing or decreasing the intensity of the action of this common agent in the exact proportions suitable for passing from one of the conditions to the other; and this is easy when it is a question of going up the scale in the case of light, and, on the contrary, it is not realizable directly, that is to say without external assistance, when it is a question of going down the scale again, in the case of heat.

3. _Heat a Degraded Form of Energy._—We have seen that thermal energy is not directly transformed into chemical energy. There is yet another restriction in the case of this thermal energy if we study the laws which govern the circulation and the transformations of thermal energy; and the most important comes from the impossibility of transporting it from a body at a lower temperature to a body at a higher temperature. On the whole, and because of these restrictions, thermal energy is an imperfect variety of universal energy, or, as the English physicists call it, a degraded form.

4. _Simple Transformations of Electrical Energy. Its Intermediary Rôle._—On the other hand, electrical energy represents a perfected and infinitely advantageous form of this same universal energy, and this explains the vast development of its industrial applications within less than a century. It is not that it is better known than the others in its nature and in the secret of its action. On the contrary, there is more dispute than ever as to its nature. To some, electricity, which is transported and propagated with the speed of light, is a real flux of the ether as was taught by Father Secchi, who compared it to a current of water in a pipe. It would do its work, just as the water of the mill does its work by flowing over a wheel or through a turbine. Electricity, like water in this case, would not be an energy in itself, but a means of transporting energy.

To others, such as Clausius, Hertz, and Maxwell, it is not so; the electric current is not a transport of energy. It is a state of the ether of a peculiar, specific kind, periodically produced (electric oscillation), and propagated with a speed of the order of that of light.

However that may be, what constitutes the essential peculiarity of electrical energy, and what causes its value, is that it is an incomparable agent of transformation. Every known form of energy may be converted into it, and inversely, electrical energy may be changed with the utmost facility into all other energies. This extreme adaptability assigns to it the part of an intermediary between the other less tractable agents. Mechanical energy, for instance, lends itself with difficulty to the production of light, that is to say, to a metamorphosis into photic energy (a variety of thermal energy). A fall of water cannot be directly utilized for lighting purposes. The mechanical work of this fall, which cannot be exploited in its present form, serves to set in motion in industrial lighting the installations, the electric machines, and the dynamos which feed the incandescent lamps. Mechanical work is changed into electrical energy, and it, in its turn, into thermal or photic energy. Electricity has here played the part of a useful intermediary.

The last part of energetics must be consecrated to the study of the general principles of this science. These principles are two in number, the principle of the _conservation of energy_, or Mayer’s principle, and the principle of the transformation of energy, or Carnot’s principle. The doctrine of energy thus reduces to two fundamental laws the multitude of laws, often known as “general,” to which natural science is subject.

§ 7. THE PRINCIPLE OF THE CONSERVATION OF ENERGY.

In all that precedes, the principle of conservation has intervened at every step. In fact, the very idea of energy is connected with the existence of this principle. We first discover the idea in the work of the philosophical mathematicians who established the foundations of mechanics:—Newton, Leibniz, d’Alembert, and Helmholtz; or of inductive physicists such as Lord Kelvin. Its experimental proof, sketched by Marc Seguin and R. Mayer, is due to Colding and Joule.

_It is Independent of the Kinetic Theory._—Mayer’s law states that energy is indestructible; that all phenomenality is nothing but a transformation of energy from one form to another, and that this transformation takes place either at equal values, or rather, at a certain rate of equivalence. This is what takes place when thermal energy is transformed into mechanical energy (equivalent 425). This rate of equivalence is fixed by the researches of physicists for each category of energy.

It will be noticed that this law and this theory of energy, which is always presented by authors of elementary books as a consequence of the kinetic theory, is quite independent of it. In the preceding lines we have not even mentioned its name. We have not assumed that all phenomena are movements or transformations of movements, whether sensible or vibratory; we have not affirmed that what was passing from one phenomenal determination to another was the _vis viva_ of the motion, as is the case in the impact of elastic bodies. No doubt the kinetic theory affords us a very striking image of these truths which are independent of it; but it may be false: and the theory of energy which assumes the minimum of possible hypotheses would yet be true.

_It contains a great many other Principles._—The principle of the conservation of energy contains a large number of the most general principles of science. It may be shown without much difficulty that, for example, it contains the principle of the inertia of matter, laid down by Galileo and Descartes; that of the equality of action and reaction, due to Newton; and even that of the conservation of matter, or rather of mass, due to Lavoisier. And finally, it contains the experimental law of equivalence connected with the name of the English physicist Joule, from which may be derived the Law of Hess and the principle of the initial and final states which we owe to Berthelot.

_It involves the Law of Equivalence._—Here we may be content with noticing that the law of the conservation of energy involves the existence of relations of equivalence between the different varieties. A certain quantity of a given energy, measured, as we have seen, by the product of two factors, is equivalent to a certain fixed quantity of quite a different form of energy into which it may be converted. The laws which govern energetic transformations therefore contain, from both the qualitative and the quantitative points of view, all the connections of the phenomena of the universe. To study these laws in their detail is the task that physics must take upon itself.

The conversion one into the other of the different forms of energy by means of equivalents is only a possibility. It is subject, in fact, to all sorts of restrictions, of which the most important are due to the second principle.

§ 8. CARNOT’S PRINCIPLE. ITS GENERALITY.

The second fundamental principle is that of the transformations of equilibrium, or of the conditions of reversibility, or again, Carnot’s principle. This principle, which first assumed a concrete form in thermodynamics, has been very widely extended. It has reached a degree of generality such that contemporary theoretical physicists such as Lord Kelvin, Le Châtelier, etc., consider it the universal law of physical, mechanical, and chemical equilibrium.

Carnot’s principle contains, as was shown by G. Robin, d’Alembert’s principle of virtual velocities, and according to physicists of to-day, as we have just remarked, it contains the laws peculiar to physico-chemical equilibrium. The application of this principle gives us the differential equations from which are derived numerical relations between the different energies, or the different modalities of universal energy.

_Its Character._—It is very remarkable that we cannot give a general enunciation of this principle which by its revealing power has changed the face of physics. This is because it is less a law, properly so called, than a method or manner of interpreting the relations of the different forms of energy, and particularly the relations of heat and mechanical energy.

_Conversion of Work into Heat and Vice-versâ._—The conversion of work into heat is accomplished without difficulty. For example, the hammering of a piece of iron on an anvil may bring it to a red heat. A shell which passes through an armour plate is heated, and melts and volatilizes the metal all round the hole it has made. By utilizing mechanical action under the form of friction all energy can be converted into heat.

The inverse transformation of heat into work, on the contrary, cannot be complete. The best motor that we can think of, and _à fortiori_ the best we can realize, can only transform a third or a fourth of the heat with which it is supplied.

This is an extremely important fact. It is of incalculable importance to natural philosophy, and may be ranked among the greatest discoveries.

_Higher and Degraded Forms of Energy._—Of these we may give an account by distinguishing among the forms of universal energy _higher forms_, and _lower_ or _degraded forms_. Here we have the principle of the _degradation of energy_ on its trial, and it may be regarded as a particular aspect of the second principle of energetics, or Carnot’s principle. Mechanical energy is a higher form. Thermal energy is a lower form, a degraded form, and one which has degrees in its degradation. Higher energy, in general, may be completely converted into lower energy; for example, work into heat: the slope is easy to descend, but it is difficult to retrace our steps; lower energy can be only partially transformed into higher energy, and the fraction thus utilizable depends upon certain conditions on which Carnot’s principle has thrown considerable light.

Thus, although in theory the thermal energy of a body may have its equivalent in mechanical energy, the complete transformation is only realizable from the latter to the former, and not from the former to the latter. This is due to a condition of thermal energy which is called _temperature_. The same quantity of thermal energy, of heat, may be stored in the same thermal body at different temperatures. If this quantity of thermal energy is in a very hot body we can utilize a large portion of it; if it is in a relatively cold body we can only convert a small portion of it into mechanical work. Thus the value of energy,—_i.e._, its capacity of being converted into a higher and more useful form,—depends on temperature.

_The Capacity of Conversion depends on Temperature._—The conversion of heat into work assumes two bodies of different temperatures, the one warm and the other cold; a boiler and a condenser. Every thermal machine conveys a certain amount of heat from the boiler to the condenser, and what is not thus carried is changed into work. This residue is only a small fraction, a quarter, or at most a third of the heat employed, and that, too, in the theoretically perfect machine, in the ideal machine.

This output, this utilizable fraction depends on the fall of temperature from the higher to the lower level, just as the work of a turbine depends on the height of the waterfall which passes through it. But it also depends on the conditions of this fall, on the accessory losses from radiation and conduction. However, Carnot has shown that the output is the same, and a maximum for the same fall of temperature, whatever be the working agent (steam, hot air, etc.), and whatever be the machine—provided that this agent, this substance which works is not exposed to accessory losses, that it is never in contact with a body having temperature different to its own—or again, that it is connected only with bodies impermeable to heat.

This is Carnot’s principle in one of its concrete forms.

A machine which realizes this condition, that the agent (steam, alcohol, ether) is in relation, at all phases of its function, with bodies which can neither take heat from it nor give heat to it, is a _reversible machine_. Such a machine is perfect. The fraction of heat that it transforms into motion is constant; it is a maximum; it is independent of the motor, of its organs, of the agent: it accurately expresses the transformability of the heat agent into a mechanical agent under the given conditions.

_The Degradation and Restoration of Energy._—The fraction not utilized, that which is carried to the condenser at a lower temperature, is _degraded_. It can only be used by a new agent, in a new machine in which the boiler has exactly the same temperature as the condenser in the first machine, and the new condenser has a lower temperature, and so on. The proportion of utilizable energy thus goes on diminishing. Its utilization requires conditions more and more difficult to realize. The thermal energy loses its potential and its value, and is further and further degraded as its temperature approaches that of the surrounding medium.

The degraded energy, theoretically, has kept its equivalent value but, practically, it is incapable of conversion. However, it is shown in physics that it can be raised and re-established at its initial level. But for that purpose another energy must be utilized and degraded for its benefit.

_The End of the Universe._—What we have just seen with respect to heat and motion is to some degree true of all other forms of energy, as Lord Kelvin has shown. The principle of the degradation of energy is very general. Every manifestation of nature is an energetic transformation. In each of these transformations there is a degradation of energy—_i.e._, a certain fraction is lowered and becomes less easily transformable. So that the energy of the universe is more and more degraded; the higher forms are lowered to the thermal form, the latter increasing at temperatures which become more and more uniform. The end of the universe, from this point of view, would then be unity of (thermal) energy in uniformity of temperature.

_Importance of the Idea of Energy in Physiology._—I have said that the application of Carnot’s principle furnished numerical relations between the different energetic transformations.

The science of living beings has not yet reached that point of development at which it is possible for us to obtain its numerical relations. However, the consideration of energy and the principle of conservation has altered the outlook of physiology on many questions which are of the highest importance.

The determination of the sources from which plants and animals draw their vital energies; the mediate transformation of chemical energy into animal heat in nutrition, or into motion in muscular contraction; the chemical evolution of foods; the study of soluble ferments—all these questions are of considerable importance when we wish to understand the mechanisms of life. They are therefore departments of physiological energetics in which great advances have already been made.