The curve 1–8 is a line which we draw freehand with a single indivisible motion of the hand and arm and eye. It is something unique and individualised, in that no other curve ever drawn, in a similar manner, exactly resembles it. Let us investigate it mathematically. We can select very small portions of it—elements we may call them—and each of these elements, if it is small enough does not differ sensibly from a straight line. Let us produce each of these straight lines in both directions, it is then a tangent to the curve, and it does actually coincide with the curve at one mathematical point—the points 1–8 in the figure. The tangent then has something in common with the curve, but would a series of infinitesimally small tangents reproduce the curve? Obviously not, for the equations of the tangents would have the form ax + b, while that of the curve itself would be quite different, containing x as powers of x, or as transcendental functions of x. In this investigation what we succeed in obtaining are the derivatives of the curve, and to reproduce the latter from its elements we have to integrate the derivatives; that is, another operation differing in kind from our analytical one must be performed. Now in this illustration we have doubtless something more than an analogy with our physico-chemical analysis of life. The activities of the organism do reduce to bio-chemical ones (the elemental straight lines on the curve), and each of these reactions has something in common with life (it is tangent to life, touching it at one point). But if we attempt to reconstitute life from its physico-chemical derivatives we must integrate the latter, and in doing so we over-pass the bounds of physics, just as integrating a mathematical function we necessarily introduce the concept of the “infinitely small.”

The physico-chemical reactions into which we dissociate any vital function of the organism have, then, each of them, something in common with the vital function. But their mere sum is not the function. To reproduce the latter we have to effect a co-ordination and give directions to these reactions. In all physiological investigations we proceed a certain length with perfect success; thus the elements, so to speak, of the function of the secretion of saliva are (1) the blood-pressure, (2) the hydrostatic pressure of the secretion in the lumina of the gland tubules, (3) the diffusibility of the substances dissolved in the blood and lymph through the walls of these vessels, (4) the osmotic pressure of the same substances, and (5) the stimulation of the gland cells by “secretory nerve fires.” Now the investigations carried out—and no part of the physiology of the mammal has been so patiently studied as the salivary gland—fail, so far, completely to describe the function in terms of these elements. In the end we have to refer the secretion to intra-cellular processes, and then we begin to invoke again processes of osmotic pressure, diffusibility, and so on with reference to the formation of the drops of secretion which we can see formed in the gland cells. We are forced to the formulation of a logical hypothesis as to the nature of these intra-cellular processes, and since much that goes on in the cell substance is, so far, beyond physico-chemical investigation, our hypothesis will be as difficult to disprove as to verify.

Let us return now to Huxley’s comparison of the activity of the green plant with the chemical reaction which occurs when an electric spark is passed through a mixture of oxygen and hydrogen. The lecture on the “Physical Basis of Life” was published in 1869; in 1852 William Thomson published his paper “On a Universal Tendency of Nature to Dissipation of Energy,” and a year or two before that Clausius had applied Carnot’s law to the kinetic theory of heat: the second principle of energetics had therefore even then been exactly formulated, but its significance for biological speculation had not been recognised by Huxley, any more than it has generally been recognised by most biologists since 1869. What, then, does the comparison of Huxley show? Clearly that the physical changes which occur in the explosion of a mixture of oxygen and hydrogen trend in a different direction from those which occur in the photo-synthesis of starch by a green plant. Generally speaking, chemical activity, that is, the possibility of occurrence of chemical reactions, is a case of the second law of energetics. Energy passes from a state of high to a state of low potential. A chemical reaction will occur if this change of potential is possible.

In all such changes energy is dissipated. What exactly does this mean? It means that, generally speaking, the potential energy of chemical compounds tends to transform into kinetic energy; while differences in the intensity factor of the kinetic energy of the bodies forming a system tend to become minimal. In a mixture of oxygen and hydrogen there is energy of two kinds, (1) potential energy due to the position of the molecules (O and H molecules are separated); and (2) kinetic energy of the molecules (which are moving about in the masses of gas). After the explosion the potential energy acquired in the separation of the molecules of O and H has disappeared (the molecules having combined to form water), but the kinetic energy has greatly increased, since the explosion results in the formation of steam at high temperature. But now this steam radiates off heat to adjacent bodies, or becomes cooled by direct contact with the envelope which contains it. The energy of the explosion is therefore distributed to the adjoining bodies, and the temperature of the latter becomes raised. But these again radiate and conduct heat to other bodies, and in this way the heat generated becomes indefinitely diffused.

The general effect of all physico-chemical changes is therefore the generation of heat, and then this heat tends to distribute itself throughout the whole system of bodies in which the physico-chemical changes occur. The energy passes into the state of kinetic energy, that is, the motion of the molecules of the bodies to which the heat is communicated. This molecular motion is least in solids, greater in liquids, and greatest in gases. If solids, liquids, and gases are in contact, forming complex systems, the kinetic energy of their molecules becomes distributed in definite ways, depending on the constants of the systems. After this redistribution the kinetic energy of these molecules is unavailable for further energy transformations, so that phenomena or change in the system ceases. There is no longer effective physical diversity among the parts of the system.

We find that this conception of dissipation of energy cannot be applied to the organism, at least not with the generality in which it applies to physical systems. Why? Not because the conception is unsound, or because the physico-chemical reactions that occur in material of the organism are of a different order from those that occur in inorganic systems—they are of the same order. The second law of energetics is subject to limitations, and it is because it is applied to organic happenings without regard to these limitations that it does not describe the activities of the organism as well as it describes those of inorganic nature.

What, then, are these limitations? We note in the first place that the laws of thermodynamics apply to bodies of a certain range of size; or at least the possibility of mathematical investigation (on which, of course, all depends) is limited to “differential elements” of mass, energy, and time. We cannot apply mathematical analysis to bodies, or time-intervals of “finite size,” since the methods of the differential and integral calculus would not strictly be applicable. But molecules are so small (1 cubic centimetre of a gas may contain about 5.4 × 10¹⁹ of them) that even such a minute part of a body, or liquid, or gas as approximates to the infinitesimally small dimensions required by the calculus, contains an enormous number of molecules.

Obviously we cannot investigate the individual molecules. Even if experimental methods could be so applied, such concepts as density, pressure, volume, or temperature would have no meaning. Physics, then, is based on collections of molecules, and the properties of a body are not those of a molecule of the same body. Such concepts as temperature and pressure are statistical ones, and are applied to the mean properties of a large number of molecules.

We can best illustrate this by considering Maxwell’s famous fiction of the “sorting demons.” Let us imagine a mass of gas contained in a vessel the walls of which do not conduct heat. Let there be a partition in this vessel also of non-conducting material, and let there be an aperture in this partition greater in area than a molecule, but smaller than the mean free path of a molecule. Now this mass of gas has a certain temperature which is proportional to the mean velocity of movement of the molecules. The second law says that heat cannot pass from a cold region in a system to a hot region without work being done on the system from outside, nor can an inequality of temperature be produced in a mass of gas or liquid except under a similar condition. But “conceive a being,” says Maxwell, “whose faculties are so sharpened that he can follow every molecule in its course; such a being, whose attributes are still as essentially finite as our own, would be able to do what is at present impossible to us.”20 For the temperature of the gas depends on the velocities of the molecules, and in any part of the gas these velocities are very different. Suppose that the demon saw a molecule approach which was moving at a much greater velocity than the mean: he would then open the door in the aperture and let it pass through from − to +. On the other hand, should a molecule moving at a velocity much less than the mean approach he would let it pass from + to −. In this way he would sort out molecules of high from those of low velocity. But the collisions between the molecules in either division of the vessel would continually produce diversity of individual velocity, and in this way the difference of temperature between + and − would continually be increased. Heat would thus flow from a region of low to a region of high temperature without an equivalent amount of work being expended.

Now we must not introduce demonology into science, so, lest this fiction of Maxwell’s should savour of mysticism, or something equally repugnant, we shall state the idea involved in it in quite unexceptionable terms. The conclusions of physics are founded on the assumption that we cannot control the motions of individual molecules. In a mass of gas, or liquid, or in a solid, the molecules are free to move and do move. Their individual velocities and free paths vary considerably from each other. These motions and paths are un-co-ordinated—“helter-skelter”—if we like so to term them. Physics considers only the statistical mean velocities and free paths. The irreversibility of physical phenomena, the fact that energy tends to dissipate itself, the second law of thermodynamics, depend on the assumption that Maxwell’s demons exist only in imagination. We must appeal to experience now. There is no a priori reason why the phenomena of physics should be directed one way and not the other, for it is possible to conceive a condition of our Universe in which, for instance, solid iron would fuse when exposed to the atmosphere. In such conditions organisms would grow backwards from old age to birth, with conscious knowledge of the future but no recollections of the past. Experience shows, however, that phenomena do tend in one way—but this experience is that of experimental physics, so that for the latter science Maxwell’s demons do not exist. Now physiology has borrowed from physics, not only the experimental methods, but also the fundamental concepts of thermodynamics. The organism, therefore (so physiology must conclude), cannot control the motions of individual molecules, and so vital processes are irreversible. But we have seen that the processes of terrestrial life as a whole are reversible, or tend to reversibility. We must therefore seek for evidence that the organism can control the, otherwise, un-co-ordinated motions of the individual molecules.

The Brownian movement of very small particles of matter is so familiar to the biologist that we need not describe it. It is doubtless due to the impact of the molecules of the liquid in which the particles are suspended. Groups of molecules travelling at velocities above the mean hit the particle now on one side, and again on the other, and so produce the peculiar trembling which Brown thought was life. Now the particle must be below a certain size in order to be so affected. Are there organisms of this size? Undoubtedly there are, for many bacilli show Brownian movements, while we have reasons for believing that ultra-microscopic organisms exist. Also, on the mechanistic hypothesis there are “biophors,” the size of which is of the same order as that of the molecules of the more complex organic compounds. All these must be affected by the molecular impacts of the liquid in which they are suspended. Can they distinguish between the impacts of high-velocity molecules and those of mean-velocity ones, and can they utilise the surplus energy of the former? This has been suggested by the physicists. In Brownian movement, says Poincaré, “we can almost see Maxwell’s demons at work.”

The suggestion is not merely a speculative one, for it is well within the region of experiment. To prove it experimentally we should only have to show that the temperature of a heat-insulated culture of prototrophic bacteria falls while the organisms multiply.

Is it not strange that the biologists, to whom the Brownian movement is so familiar, should have failed to see its possibly enormous significance? Is it not strange that the biologists, to whom the distinction between the statistical and individual methods of investigation is so familiar, should have failed to appreciate this distinction when it was made by the physicists? Is it not strange that while we see that most of our human effort is that of directing natural agencies and energies into paths which they would not otherwise take, we should yet have failed to think of primitive organisms, or even of the tissue elements in the bodies of the higher organisms, as possessing also this power of directing physico-chemical processes?