So with the powder in a gun. The potential energy of the powder cannot become actual without some stimulus, some exciting force from without to set it free. It is the external work of pressing the trigger that liberates the potential energy of the powder, transforming it into the actual energy of combustion, and the kinetic energy of the projectile.

Since energy is work, and work is a function of motion, there is in reality no such thing as energy in repose. Matter according to our modern conception is a complex of molecules, atoms, and electrons; we conceive the molecules of matter as always in movement, animated with cyclic or vibratory motion, these oscillatory or rotatory movements representing the potential energy of the body in question. Potential energy is thus the expression of molecular motion without translation of the molecules as a whole in s.p.a.ce.

When this potential energy is transformed into actual energy by the intervention of some external force, we get a current of energy, a transference of the molecules in s.p.a.ce. Thus, when an external force has released the weight, the molecular orbits in the falling body change in form, and the potential energy of the molecular motion becomes the kinetic energy of the falling body. Similarly in the conduction of heat, the energy of the hot body is transferred to a colder body by transmission of the vibratory motion from molecule to molecule. So again with chemical energy, the molecular motion of combustion may be transformed into the radiant energy of the ethereal waves.

Actual energy may be regarded as a current of molecular motion. To make the matter clearer, let a ma.s.s of matter be represented by a regiment of soldiers. Then each soldier will represent an electron, a company will be an atom, and a battalion will be a molecule. As long as the soldiers mark time, turn, or otherwise exercise without advancing, we have simply an acc.u.mulation of potential energy. The word of command, "March," is the exciting force which suddenly transforms this potential into kinetic energy. The marching {102} regiment is a representation of a body possessing kinetic energy. Potential energy is energy confined to a certain point in s.p.a.ce, whereas actual energy is a current of energy, continually changing its place or form. Energy is like water-power--potential in the lake, actual in the waterfall or river.

Any mechanism capable of causing one form of energy to pa.s.s into another is a transformer of energy. A steam engine is a transformer of energy, changing caloric energy into mechanical work. An electrical machine is a transformer of energy, converting mechanical motion into a current of electricity, whilst an electro-motor changes the movement of electrons into mechanical movement. Every living being, and even man himself, is but a transformer of energy, changing the energy derived from the earth and air and sun into mechanical motion, nervous energy, and heat.

The first law of energetics, that of the conservation of energy, is a.n.a.logous to Lavoisier's principle in chemistry, the conservation of matter. The sign of equality which unites the terms of a chemical equation expresses the fact that after every chemical reaction the same total ma.s.s of matter is present as before the transformation. This is also true of energy; after every transformation we find exactly the same total quant.i.ty of energy as before it. This, however, tells us nothing as to the conditions of the transformation, or the causes, _i.e._ the anterior phenomena, which determined such transformation.

The second principle of energetics, that of Carnot, enunciated in 1824, deals with the conditions under which a transformation of energy is possible. A ma.s.s of water at a certain height represents a quant.i.ty of potential energy equal to the product of its weight by its height; but this energy cannot produce mechanical work unless the water is allowed to fall.

Consider two lakes at the same alt.i.tude and of the same capacity, one of which is entirely landlocked, while the other has an open channel leading to the sea. Each lake represents the same quant.i.ty of potential energy, but the energy of the landlocked lake is useless, it cannot be {103} transformed; whereas the other lake whose water can run into the sea realizes the conditions necessary for utilization, viz. the transformability of its energy. The same may be said of all forms of energy; a heat engine can only act as a transformer, change heat into work, if there is a difference of temperature between its source and its sink; an electric motor can only work if there is a fall of potential between the entrance and the exit of the electric current.

Energy presents itself to us as the product of two factors, weight and height in the waterfall, quant.i.ty and temperature in the heat engine, current intensity and potential in the electric motor.

In considering these two factors we may note that one factor is always a quant.i.ty (Q) and the other an intensity (I). This latter expresses some sort of difference of position or condition, the height of the weight, a difference of temperature in the heat engine, of pressure in the gas engine, or of electric potential in the dynamo or electric furnace. There can be no current of energy without this difference of potential, and therefore no transformation from one form of energy to another.

The second law of thermodynamics, Carnot's law, may therefore be enunciated thus: "Energy cannot be transformed without a fall of potential."

We may also derive this principle from a consideration of the formula of efficiency, the ratio of the work done by the transformer to the work done on the transformer.

Efficiency = energy transformed / total energy absorbed

The total energy is the product QI, _i.e._ the product of the total quant.i.ty by the total intensity at our disposal. The transformed energy is Q(I - I'), the product of the total quant.i.ty by the difference of intensity at the inlet and at the outlet of the machine. The formula for efficiency thus becomes

Q(I - I') / QI = (I - I') / I.

If I represents a temperature, then in order that the efficiency may be positive I' must be less than I, {104} there must be a fall of temperature in the machine. If I' were greater than I, _i.e._ if the temperature at the outlet were greater than that at the inlet, the efficiency would be a negative one, and the transformer would have to borrow heat from some external source.

_Entropy._--In every transformation of energy a certain portion of the energy is transformed into heat: a lamp gives out useless heat as well as light, a machine gives out useless heat as well as mechanical work. This loss of useful energy as heat occurs in every transference or transformation of energy; it is only in the case of heat pa.s.sing from a hotter to a colder body that there is no such transformation. When equality of temperature is established there has been no loss of energy, but the whole of the energy has become unutilizable, i.e. untransformable. In the formula of efficiency the fall of intensity I - I' is now zero, and therefore the efficiency of the machine

(I - I') / I

is also zero.

Since in all its transformations a certain fraction of the energy is changed into heat, there is a tendency in nature for all differences of temperature to become equalized. Hence the quant.i.ty of utilizable energy in the universe tends to diminish. Clausius called this unutilizable energy enmeshed in the substance of a body its entropy, and showed that in every transformation the amount of this unutilizable energy tended to increase.

"The entropy of a system always tends towards a maximum value."

If this gradual incessant increase of entropy is universal in nature, and if there is no compensatory mechanism, the universe must be tending towards a definite end, when the whole of its energy shall have been transformed into unutilizable heat with a uniform temperature. There is, however, reason to suppose that some such compensatory mechanism does in fact exist.

Behind us stretches an infinite past, and in the future we believe that the phenomena of nature will be unrolled in a cycle which has no end. But the arguments derived from a study of entropy apply only to the facts and phenomena actually under our notice, the supposed {105} impossibility, without borrowing energy from without, of re-establishing the differences of temperature by drawing heat from a colder in order to concentrate it in a hotter body, and may not be absolutely identical with those obtaining in other ages. Our ignorance of such a phenomenon and our powerlessness to produce it in no way argue that it is impossible. It may exist for aught we know in some other region of s.p.a.ce, or in another time than ours. We may perhaps some day obtain artificially the conditions which would render possible such a phenomenon, since it may be possible to produce in the experimental laboratory conditions which are not spontaneously realized in nature under present conditions. The future may perchance reveal to us absolutely new phenomena which have not hitherto been realized. In his work on the evolution of matter and of energy Gustave le Bon gives expression to some interesting and original ideas on this subject.

The laws of Mayer and Carnot alone are not sufficient to explain the phenomena of life, without some consideration of the laws of stimulus.

Mayer's principle a.s.serts the conservation of energy, and Carnot's the conditions necessary for its transformation, but these alone cannot account for the transformation of potential into actual energy. A weight suspended by a cord does not fall merely because there is room for its descent. We need the intervention of some outside force to cut the cord. In every transformation of energy this external force is required to cut the cord, or pull the trigger, some external force of excitation or liberation, an energy which may be infinitesimal in amount, and which bears no proportion to the quant.i.ty of potential energy it sets free. This intervention of an excitatory, stimulating, or liberating energy is universal. Every phenomenon of nature is but a transformation or a transference of energy, determined by the intervention of a minimal quant.i.ty of energy from without. This liberation of large quant.i.ties of potential energy by an exceedingly small external stimulus has not hitherto received the consideration it demands. Certain phenomena, such as those of chemical catalysis or the action of soluble ferments, excite our astonishment because such extremely small quant.i.ties of {106} certain substances will determine the chemical transformations of large quant.i.ties of matter, there being no proportion between the amount of the catalytic substance and of the matter transformed. These phenomena are, however, only particular cases of the general law of energetics that transformation requires a stimulus.

The catalyzer, or ferment, does not contribute matter to the reaction, but only the minimal energy necessary to liberate the chemical potential energy stored in the fermenting substance.

We must therefore add a third to the two laws of energetics, Mayer's law of conservation, and Carnot's law of fall of potential. This third law is the law of stimulus, the necessity of the intervention of an external excitatory force capable of setting in motion the current of energy required for a transformation. This stimulus is the primary phenomenon, the determinant cause of such transformation.

Three conditions, then, are required for a transformation or displacement of energy:--

1. _The cause_, the intervention of a stimulus which starts the transformation or displacement.

2. _The possibility_, the necessary fall of potential.

3. _The condition_, the conservation of the energy concerned, since being indestructible its total quant.i.ty cannot alter.

Every living being is a transformer of energy. The lower animals and man himself receive from food and air the potential energy which becomes actual under the process of oxydation. This chemical combustion is the source of all vital energy; the ancients aptly compared life to a flame, and Lavoisier has shown that life, like the flame, is maintained by a process of oxydation. The energy derived from food and air is restored by the organism to the external world in the form of heat and mechanical motion.

The celebrated experiments of At.w.a.ter show that there is an absolute equality between the energy obtained from the oxydation of the various aliments and the sum of the calorific and mechanical energy liberated by a living being.

Man obtains his supply of energy either directly from the {107} vegetable world, or indirectly from vegetables which have pa.s.sed through the flesh of animals. Vegetables in their turn obtain their substance from the mineral world and their energy from the sun. The salts, the water, and the carbonic acid absorbed by plants possess no store of potential energy. Whence then can they obtain the potential energy which they transmit to animals and man, if not from the sun? The energy of the solar radiations is absorbed by the chlorophyll of the leaves, and stored up in the organic carbohydrates formed by the synthesis of water and carbon. Chlorophyll has the peculiar property of reducing carbonic acid, and uniting the carbon with water in different proportions to form sugar and starch, whilst fats and vegetable alb.u.mens are also formed by an a.n.a.logous reaction. All these complex bodies are stores of energy; the vital processes of oxydation do but liberate in the human body the energy which the chlorophyll of plants has absorbed from the solar rays.

We must look, then, to the sun as the direct source of all the energy which animates the surface of the earth. The sun looses the winds, and raises the waters of the sea to the mountain-tops, to form the rivers and torrents which return again to the sea; the sun warms our hearths, drives our ships, and works our steam engines. There is no sign of life or movement on our planet which does not come directly or indirectly from the solar rays.

It may be asked by what path does the chemical energy of the living organism pa.s.s into the mechanical energy of motion. It would appear that the intermediary step cannot be heat, as in the steam engine, since the necessary temperature would be quite incompatible with life.

The formula for the efficiency of a thermic transformer is

(T - T') / T,

the ratio of the difference of the absolute temperatures at the source and at the sink, to the absolute temperature at the source. Calorimetric measurements have shown that the efficiency of the human machine is about one-fifth, _i.e._ it can transform 20 per cent. of the energy absorbed. The ordinary temperature of muscle is 38 C., or 311 absolute. We have {108} therefore (T - 311) / T = .20, or T = 388.75 absolute, _i.e._ 115.75 C.

Thus, in order to obtain an efficiency of 20 per cent. with an ordinary thermic transformer, having a temperature of 38 at the sink, we should need a temperature of over 115 C. at the source. Such a temperature would be quite incompatible with the integrity of living tissues, and we may therefore conclude that the human organism is not a heat engine.

We are indeed completely ignorant of the mode of transformation of chemical into kinetic energy in the living organism; we know only that muscular contraction is accompanied by a change of form; at the moment of transformation the combustion of the muscle is increased, and during contraction the stretched muscular fibre tends to acquire a spherical shape. It is this shortening of the muscular fibre which produces the mechanical movement. The step which we do not as yet fully understand is the physical phenomenon which intervenes between the disengagement of chemical energy and the occurrence of muscular contraction. Professor d'Arsonval supposes that this missing step is a variation in the surface tension of the liquid in the muscular fibre. The surface tension of a liquid is due to the unbalanced forces of cohesion acting on the surface layer of molecules. Under the attraction of cohesion the molecules within the liquid are in a state of equilibrium, being equally attracted in all directions, but those at the surface of the liquid are drawn towards the centre. The resultant of these attractive forces is a pressure normal to the surface, which is mechanically equivalent to an elastic tension tending to diminish the surface. In consequence of this surface tension the liquid has a tendency to a.s.sume the form in which its surface area is a minimum, _i.e._ the spherical form. If such a sphere is stretched into a cylinder or fibre by mechanical tension, it will shorten itself when released; and if by any means we increase the surface tension of such a liquid fibre it will tend to a.s.sume a spherical form and contract just as a muscular fibre does.

The surface tension of a liquid varies with its chemical composition; the slightest chemical modification of a liquid alters the force of {109} this tension. We may therefore explain the mechanism of muscular contraction by supposing that a nervous impulse alters in some way the rate of combustion in a muscular fibre, that this alteration produces a momentary change in the chemical composition of the muscular cell, and that this change of chemical composition increases the surface tension of the cell sufficiently to provoke its contraction into a more spherical form.

Ostwald has introduced a very useful conception for the study of this question of surface energy. A liquid surface contains a quant.i.ty of energy equal to its surface tension multiplied by its area, hence any variation either of area or of tension corresponds to a variation of its energy. This novel conception const.i.tutes a valuable addition to the experimental study of the physiology of muscular action, since it gives us some idea of the mechanism by which chemical energy may be transformed into muscular contraction.

Whatever the mechanism of transformation in the animal machine, we have to consider the same quant.i.ties as in other motor machines. These are: (1) the efficiency; (2) the potential energy; (3) the power; (4) the energy given up to the medium under the form of heat; (5) the temperature.

Muscles, then, are merely transformers which change chemical energy into mechanical work, the diminution of stored-up energy in a muscle being expressed by the sensation of fatigue. A muscle may be studied in four different phases: (1) in repose; (2) in a state of tension; (3) when doing positive work; (4) when work is being done on it.

When a muscle is in a state of tension, as when a weight is sustained by the outstretched arm, the muscle is producing no external work. The entire work done is converted into heat; just as it is in a dynamo or steam engine which is prevented from turning by a brake. Muscular contraction produces fatigue even when it does no external work. It is impossible for the muscle to support even the weight of the outstretched arm itself for any considerable time.

A muscle is doing positive work when it is raising a weight or moving a body from one point to another. {110}

The fourth state of muscular contraction is when the muscle is doing negative work, _i.e._ when work is being done on it, as for instance when we go downstairs, or when a descending weight forces down the opposing arm which attempts to support it. In this case the muscles receive a portion of the energy lost by the descending weight, and this energy shows itself in the muscle in the form of heat. This increase of heat in a muscle doing negative work has been clearly demonstrated by the calorimetric experiments of Hirn and the thermometric experiments of Beclard. Hirn's observations on muscular calorimetry show a production of heat corresponding to 150 calories per hour when in repose, 248 calories per hour during positive work, and 287 during negative work. Beclard's thermometric measurements also show that the temperature of a muscle rises each time that it contracts, and that the rise of temperature is greatest when the muscle is doing negative work, least during positive work, and intermediate when in a state of tension.

It is of the greatest importance in medical practice to distinguish between these different forms of muscular activity. There is a vast physiological difference between muscular contraction with the production of positive work, and muscular contraction without the production of work, or with negative work. To climb a flight of stairs is to contract the muscles with the production of work equal to the weight of the body multiplied by the height of the stairs. To descend the stairs is to contract the same muscles, but with the production of negative work, and consequently a maximum of heat. To walk on level ground is to contract the muscles with the production of little or no external work; as in a machine turning without friction in a vacuum.

We have seen that a fall of potential and a current of energy are the necessary conditions for the production of any natural phenomenon. Hence we may a.s.sume that the phenomenon of sensation is also accompanied by a fall of potential and a current of energy. When we touch a hot body, there is a flow of energy from the hot body to the hand. When we touch a cold body, there is a current of energy in the opposite direction, {111} from the hand to the body. It was formerly held, and is still held by some physiologists, that the chief characteristic of life is the disproportion between an excitation and the response which it invokes from the organism. Such a doctrine can only be held by one who believes, at least implicitly, that the phenomena of life are supernatural, or at all events different in their nature from all other phenomena; for the disproportion between an excitation and the response it evokes is by no means confined to living things. This disproportion is universal in nature, and quite in conformity with the physical laws which govern the transformation of energy. The energy of living things is potential energy--a fact which has been too little recognized. In the case of reflex actions it is self-evident, because the response is immediate, and always the same for the same stimulus. As in all other transformations, the stimulus consists in the intervention of a minimal quant.i.ty of external energy.

Long before the discovery of the laws of energy, Lamarck had recognized and formulated this fact. He writes: "What would vegetable life be without excitations from without, what would be the life even of the lower animals without this cause?" In another pa.s.sage, seeking for a power capable of exciting the action of the organism, he says: "The lower animal forms, without nervous system, live only by the aid of excitations which they receive from without. In the lowest forms of life this exciting force is borrowed directly from the environment, while in the higher forms the external exciting force is transferred to the interior of the living being and placed at the disposal of the individual."

This remark, that the movements of living things are not communicated but excited, that the external excitation only sets free latent or potential energy in the organism, shows that Lamarck had penetrated more deeply than many of the modern physiologists into the secrets of biological energy. We seek in vain in the text-books of physiology for any conception of potential energy in living beings, or the notion of an exciting force as the cause of sensation. All action of a living organism is reflex action.

Every action has a cause, and {112} the cause of an organic action is an exciting energy from without, either immediate, or stored up in the nervous system from an external impression made at some previous epoch. Actions which are not evidently reflex are merely delayed reflexes; we have acquired the power of inhibiting, delaying, or modifying the response to an external stimulus, so that the same excitation may determine responses of very different kinds according to the mood produced by previous impressions. When carefully investigated, no action of ours is automatic; every movement is determined by impressions derived from without. An action without a motive, that is without an external determining cause, would be an action without reason.

In conclusion, we may formulate this general principle: The energy of a living being is potential energy; sensations represent the intervention of an external exciting energy which provokes the response, _i.e._ the transformation of the potential energy already stored in the organism into the actual energy of motion and vital activity.