CHAPTER VIII. The Organic and the Inorganic

THE ORGANIC AND THE INORGANIC

It is convenient that we should express the results of biological investigation in schemes of classification, for only in this way can we reduce the apparent chaos of naturally occurring organic things to order, and state our knowledge in such a way that it can easily be communicated to others. But we must always remember that the classifications of systematic biology are conceptual arrangements, depending for their precise nature on the point of view taken by their authors. The clear-cut distinctions that apparently separate phylum from phylum, class from class, order from order, and so on, do not really exist. There are no such categories of organisms in nature as genera, families, and the higher groupings. All that we can say exist naturally are the species, since all the organisms composing each of these groups are related together by ties of blood-relationship, and all are isolated from the organisms composing other species by physiological dissimilarities which render the plants or animals of one species infertile with those of any other. Such would doubtless have been the opinion of most botanists and zoologists prior to the work of de Vries, but we must now recognise that the systematic, or Linnean, species of the nineteenth century was just as artificial a category as were the genera and families. Our arrangements of plants and animals into systematic species and the higher groupings are therefore convenient ways of symbolising the results of morphological and physiological investigations, although they also indicate the main directions taken by the evolutionary process, but the manner in which they are stated in taxonomic schemes is always a more or less formal one.

There are no absolute distinctions between group and group, even between the animals and the plants. There is nothing, for instance, in the morphology of a Diatom to indicate that it belongs to the vegetable kingdom, or in that of a Radiolarian, to indicate that it is an animal. Peridinians are either plants or animals according to the general argument, or the point of view of the author who writes about them. Even a study of the energy-transformations that are effected in the living substance of these lower organisms does not afford an absolute distinction: synthetic metabolic processes in which energy passes into the potential condition may be carried out in animals, while many plants--the saprophytic fungi, or the insectivorous plants, for instances--may effect analytic energy-transformations of essentially the same nature as those exhibited in the typical mode of animal metabolism. Motility and the possession of a sensori-motor system do not afford the means of making a sharply drawn line of division between plants and animals. Potential energy passes into the condition of kinetic energy in the typical animal, and this kinetic energy is directed by the sensori-motor system. But some lower unicellular plants are motile, and they possess the rudiments of a sensori-motor system in the flagella by which their movements are effected. On the other hand, the sensori-motor system has become vestigial in many animal parasites--in the Crustacean Sacculina, for instance, which is parasitic on some Crabs. The possession of consciousness, in so far as we can say that other animals than ourselves possess it, is no distinction between the two kingdoms of life. Consciousness, judged by the degree of development of motility, must be supposed to be absent or very dim in the extreme cases of parasitism attained by some animals; on the other hand, we may assume that it is present, to some extent at least, in the highly motile zoospores of the Algæ. Thus some lower organisms, the Peridinians and the algal spores, exhibit all the characters which we utilise in separating animals from plants--the chlorophyllian apparatus, by means of which the kinetic energy of solar radiation becomes transformed into the potential energy of organic chemical compounds; the apparatus of receptor and motile organs, by means of which the potential energy of stored chemical compounds passes into the kinetic energy of bodily movements; and the existence (so far as we can say that it exists in organisms other than ourselves) of some degree of consciousness.

Neither do those morphological schemata which we construct as diagnostic of phyla, or classes, or orders, etc., separate these groups from each other so clearly and unequivocally as our classifications suggest. It might seem for instance that the presence or absence of a notochord would sharply distinguish between the vertebrate and invertebrate, but structures which suggest in their development the true notochordal skeleton of the typical vertebrate animal are to be traced in animals which exhibit few or none of the characters which we regard as diagnostic of the Vertebrate. Typical Arthropods and typical Vertebrates seem to be distinct from each other, but the extinct Ostracoderms of Silurian times may have been animals which possessed an internal axial skeleton, and which were also armed by a heavy dermal exo-skeleton. It is a hypothesis of considerable plausibility that they really were Arthropods, on the other hand they are usually regarded as Vertebrates. So also with most other phyla: the morphological characters which absolutely distinguish between one group and others are very few indeed, and the small appended groups that lie about the bases of these larger groups may present one or other of the characters of several phyla. Looking at the morphology of the animal kingdom in a general kind of way, one does indeed see that a certain structural plan is characteristic of the organisms belonging to each of the great phyla, while more detailed structural plans may be said to be characteristic of the sub-groups. But minute morphological and embryological investigation reduces almost to nothing the characters which are absolutely diagnostic of these various groups.

No more than the nature of the energy-transformations, and the essential morphology, does the behaviour of animals afford us the means of setting up absolute distinctions between group and group. Really tropistic behaviour is exhibited by the movements of the stems, roots, and leaves of green plants, or in the movements of Bacteria, and perhaps some unicellular animals. Typically instinctive behaviour is exhibited by the individuals of societies of Insects and by many solitary-living animals belonging to this class; and typically intelligent behaviour is exhibited by the acting of the higher Mammalia. Yet there is undoubtedly much that is truly instinctive in the behaviour of Man, and something of the same nature as his intelligence seems to inhere in the instinctively-acting mammal or insect: how else could an instinctive action become capable of improvement? We cannot doubt that intelligence is manifested by a dog or by much that we see in the behaviour of ants. No rigid distinctions between tropisms, such as we have mentioned above, and the reflexes that may be taken to constitute instinctive behaviour, can be established. Minute analysis, such as that carried out by Jennings on the swimming movements of the Protozoa, leaves us quite in doubt as to how these modes of behaviour are most properly to be described; and all the controversy as to the nature of tropisms, reflexes, instinct, and intelligence surely indicates that these modes of behaviour have something that is common to all of them, and that no clear and certain distinction can be said to separate one from the other. Even those psychic processes which we call intellectual do not seem to be different in kind from some that we attribute to the lower animals: the Protozoan Paramœcium studied by Jennings, or the crabs, crayfishes, and starfishes studied by Yerkes and others really learn to perform actions, but this learning is said to be the result of a process of “trial and error.” The animal tries one series of movements and finds that it fails, tries another and another with a similar result, and in the end finds one that is effective. This is remembered, and when the same problem again confronts the animal it is solved after fewer trials, and finally, after experience, the end-result is attained at once without previous trials. Now many of what we call truly intellectual processes are certainly processes of precisely this nature. Hypothesis after hypothesis occurs to the scientific man (or to the detective, or to the engineer confronted with some exceptional difficulty), and one after another is tested by actual trial, or by a process of reasoning (which is really the rapid and formal resuming of previous experience), until a hypothesis verifiable, or a priori verifiable, is found. What, for instance, are our mathematical methods of integrating a function, or working a long division sum, but methods of scientific “guessing,” and verification of the hypotheses so made? They are truly instances of the method of trial and error practised by the lower animals.

All the above amounts to saying that there is a community of energetic processes, of morphology, and of behaviour in animals and plants. “Protoplasm” is the same, or much the same chemical aggregate, whether it is contained in the cells of animals or plants. The cell, with its nucleus, chromatic architecture, cell-inclusions, and cell-wall, is essentially the same structure in all organisms. The complex and specialised process of nuclear division in tissue growth, or the series of events which constitute the acts of fertilisation of the ovum or its plant correlative, are the same all through the organic world. The sensori-motor system--receptor organ, nerve-fibre and cell, and effector-motor organ--is the same all through the animal kingdom. Alimentary canal and glands, enzymes, excretory tubules, contractile blood-vascular apparatus--all these are structures which are functionally the same, which are built on essentially the same morphological plan. Life, whether it is the life of plant or animal, makes use of the same material means of perpetuating itself on the earth and avoiding the descent of matter towards complete inertia.

Absolute dissimilarities, dissimilarities such as those between atoms of hydrogen and oxygen, or between a point and a straight line, or between rest and motion, do not exist between the different categories of entities that make up the organic world. Yet differences do exist, and must we conclude that because these differences are not absolute ones, because they are differences of degree, and not of kind, they are not essential, are not differences at all? Must we say, for instance, that although an animal is a much more efficient machine than a gas-engine (in the sense of efficiency as understood by the engineer), there is really no difference between them, that they are both thermo-dynamic mechanisms, since in both energy is dissipated? Ought we to say that, because the last steps in the formation of urea in the animal body are synthetic ones, there is really no difference between the nature of the energy-transformations that occur in the animal and the plant modes of metabolism? Ought we to say that, because a dog may sometimes act intelligently and a man instinctively, psychically they are similarly-behaving organisms? Surely this amounts to saying that, because things are not absolutely different, they are the same; and surely the mode of reasoning is a vicious one!

What we clearly see in the different kinds of organisms--in the metabolically constructive plant and the metabolically destructive animal; or in the instinctively-acting Arthropod and the intelligently-acting Mammal--is the progressive development of different tendencies. If the green plant is, in its essence, the same kind of physico-chemical constellation as is the animal, yet the tendency of its evolution has been that more and more it has acquired the habit, or the power, of using solar radiation to combine together carbon dioxide, water, and nitrogenous inorganic salts to form proteid and carbohydrate substances. On the other hand, the tendency of the animal has been more and more to absorb into its own tissues the proteid and carbohydrates synthesised by the green plant, and then to break these substances down into carbon dioxide and water, and less and less to effect such syntheses as are effected by the plant. Even if the Annelid worm, the Arthropod, and the Vertebrate were, at the origin of their ancestries, animals which were very like each other in the morphological sense; even if there are some Arthropods which are very like Annelids, and some Annelids which might very easily be imagined to become transformed into Vertebrates, and some extinct Arthropods which may after all have been Vertebrates, yet it is the case that the tendencies of the evolution of each of these groups have been very different. All the while the Vertebrate tended more and more to develop a rigid axial rod or notochord, becoming later a jointed vertebral column, and a soft, pliable, exo-skeleton; while the Arthropod tended more and more to develop a rigid exo-skeleton, and to remain soft in its axial parts. Even if these two tendencies may not have been fully realised, is it not the case that they are really different things? The evolutionary process has therefore been, in its essence, the development, or unfolding, of tendencies originally one.

What is the evolutionary process? It is usually regarded as a progress from organic simplicity towards organic complexity. Yet if we think about it as a physical process we cannot say that any one stage is any more simple or complex than any other stage. Let us compare organic evolution with the process of inorganic evolution, as, of course, we are compelled to do if we regard the former process as a physico-chemical one. Assume, then, that the nebular hypothesis of Kant and Laplace is true--it will make no difference to our argument even if this hypothesis is not true, and it is more easily understood than any other hypothesis of planetary evolution. Originally all the materials composing our solar system existed in the form of a gaseous nebula possessing a slow rotatory motion of its own. It does not matter that the silicates, carbonates, oxides, and all other mineral substances that we now know existed then in the form of chemical elements, or the precursors of chemical elements: all the material bodies now present in the solar system were present in the original nebula. The energy of this nebula consisted of the potential energy represented by the separation of atoms which later on became combined together, and of the kinetic energy of motion of these atoms; and this material and energy, together with the other cosmic bodies radiating energy to it and those bodies receiving the energy which it lost by its own radiation, constituted a system, in the sense of the term as it is employed by the physicists. Now, in the process of cosmic evolution this system became transformed, because it was continually losing energy by radiation. As it cooled, the mean free paths of its atoms and molecules became less and less, and finally condensation to the liquid and then to the solid condition occurred. The parts of the nebula continually gravitated together, so that it became smaller and smaller while its rotatory motion became greater. Finally, mechanical strains became set up in its mass as the consequence of the increased velocity of rotation, and disruption occurred with the formation of the sun, the planets, and the satellites. There was no increase of complexity of the system. At any moment of time its elements, that is, the chemical atoms composing it and the energy of these atoms, was the same as at any other moment of time. Heat-energy may have been radiated from one part of the system--the heated nebula--to some other part of the system--the other cosmic bodies absorbing this radiation, but the total energy of the system remained the same. The chemical atoms may have combined together to form molecules and compounds, and their energy of position may have become the energy of motion, but the ultimate materials were still the same. What happened during the cooling and contraction of the nebula was a rearrangement of the elements of the system, that is, of the atoms and their energies. At any moment of time the condition of the system was an inevitable consequence of the condition at the moment immediately preceding this, and a strict functionality, in the mathematical sense, existed between the two conditions. It was not more complex in the later stage than in the earlier one--it was merely different. Stages of evolution were really phases in a transforming system of matter and energies.

If we choose to regard organic evolution as a similar process of physico-chemical transformation, we must also regard the totality of life on our earth, with all the inorganic materials which interact with organic things, and with all the energies, cosmic and terrestrial, which also so interact, as a system in the physical sense. We are now compelled to think about this system in the same way as we thought about the cosmic one, that is, we must postulate that a rigid mathematical functionality existed between any two conditions of it, and that the latter condition was inevitably determined by the former one. We must think of the system as at all times composed of the same elements. In its later condition life may have been manifested in a greater mass of material substance than in its earlier conditions, but this increase of mass was only the increase of one part of the system at the expense of another part. At all times, then, the constitution of the system was the same, and different stages of the evolutionary process have only been different phases, or arrangements, of the same elements. At no time was the organic world any more or less complex than at any other time. In its “primitive” condition all was given.

Mechanistic biology does not, of course, hesitate to accept this view of the evolutionary process. The “Laplacian mind” must have been able to calculate what would be the condition of the system at any phase, knowing the positions of all the atoms or molecules in the original nebula, and the velocities and directions of motions of all these atoms or molecules. Just as (in Huxley’s illustration) a physicist is able to calculate what will be the fate of a man’s breath on a frosty day, so the Laplacian mind must have been able to predict the fauna and flora of the world in the year 1913 from a complete knowledge of the material nature and energetic properties of the nebula from which it arose.

We cannot fail to see, on reflection, to what this view of the nature of the evolutionary process leads us. The primitive world-nebula was a system of parts which had extension in space. Materially it consisted of atoms isolated from each other by space, and energetically it consisted of the movements of these atoms, and of the energy of their positions with regard to each other. No two atoms could occupy the same space--they mutually excluded each other: this is what we mean by saying that the original--and every other--state of the system was a state of material things or elements spatially extended. Therefore, if the physical analogy is consistently to be retained, the organic system undergoing evolution was a system of elements which at any moment whatever were spatially extended. It was really a system of atoms or molecules possessing kinetic energy of motion, or potential energy of position--molecules which lay outside each other, and energies which were really the movements or positions of these molecules, and which therefore lay outside each other in the same sense.

The evolution of the individual organism must be a process of the same kind. Like cosmic and phylogenetic evolution, it is apparently a progress from the simple to the complex. A minute fragment of protoplasmic matter, homogeneous in composition, or apparently so, grows and differentiates, becoming the complex structure of the adult organism. Here the system in the physical sense is the fertilised ovum, the oxygen and nutritive matter which have become incorporated with it, and the physical environment with which these things interact. All these elements existed in that phase of the system which contained among its parts the fertilised ovum, as well as in that phase which contained the fully developed organism. Complex by comparison with the fertilised ovum and its environment as the adult animal and its environment may seem to be, it is only a different phase of the same system. Further, all the parts that form the tissues of the adult, and all their motions, are spatially extended, and are only rearrangements of the molecules and of the motions of the molecules that were actually present in the system in its initial phase. Speculation along these lines has led to all the results of Weismannism. All the parts of the adult organism are really present in the fertilised ovum and the nutritive matter which is to build up the fully developed animal, not in potentiality it must be noted, but actually present in the spatially extended condition. It is true that the hypothesis only requires that the determinants of the adult organs and tissues, and of the adult qualities, should be present in the ovum; but since the energies necessary for the separation of these determinants, and for their arrangement and growth in mass, must also be present in the initial phase of the system, it is evident that the hypothesis implies that all the material structure of the animal is present in the spatially extended form in the initial phase of the system. Just as the adult animal is a manifoldness of material parts and energies that possess extension, so also is the undifferentiated embryo and its material environment an extensive manifoldness. We cannot otherwise conceive it if we are to retain the mechanistic view of the development of the individual organism.

Let us think of the process of organic evolution in another way by comparing it with the mathematical process by which we form the permutations and combinations of a number of different things. Individual development is termed the assumption of a mosaic structure, that is, all the parts of the adult are assumed to be present in the embryo, but in a sort of “jumbled-up” condition. As development proceeds, these parts become sorted out and arranged in a pattern which continually becomes more and more distinct. Much the same process of arrangement and segregation must be assumed to have occurred during the process of racial evolution: the parts of the “primitive” life-substance, with all the parts of the physical environment which become incorporated with it during its evolution, must have become segregated and arranged so as to form the existing species of plants and animals. A permutation, then, of the separate things a, b, c--x, y, z, is an arrangement of all these things: obviously there are a very great number of ways in which the letters of the alphabet may be arranged, 26! in all. But we may take some of the letters and arrange them in different ways: the selections a, b, c, d, can be arranged in 4! ways b, c, d, e, also in 4! ways, and so on. Thus by a process of dissociation and arrangement of a certain number of elements, a very great number of different things--things which consist of elements spatially extended--can be obtained.

The group of things, a, b, c, d--x, y, z, was an extensive manifoldness, since it was formed by juxtaposing in space the separate units of which it is composed. Yet it is an unitary thing, for it is a different thing from the group, b, c, a--x, y, z. It is also a multiplicity, for it can be transformed into every one of the 26! permutations, and broken up into the selections of some of the separate things of which it is composed, and of the permutations of the things taken in each of these selections. In a way these arrangements exist in the group a, b, c--x, y, z, and yet the group itself possesses no other actual extended existence than the group of things that it is. It is an intensive multiplicity or manifoldness in that the potentiality of all the arrangements exists in it but not in the spatially extended condition. It is a multiplicity only when we associate with it the mental operations by which we conceive of its dissociation and rearrangement. By reason of these mental operations the intensive multiplicity of the group becomes the extensive multiplicity of its arrangements.

This appears to be the only really philosophical way in which we can attempt to picture to ourselves the processes of individual and racial evolution. The “primitive” life-substance, or the undifferentiated ovum, each of them with its environment, was an intensive manifoldness, a multiplicity of distinct things or qualities which co-existed, and which were not separate each from other in that they occupied different compartments of space, but which interpenetrated each other. This notion of distinct things co-existing in time, yet occupying the same space, is not at all a difficult one. Our consciousness is such a multiplicity of states or qualities all in one. The idea of a group of figures has a very real existence for the sculptor, and he may visualise it with almost all the appearance of reality that the actual, material piece of statuary possesses. In his mind it is a real manifold existence, which nevertheless does not occupy the three-dimensional space which the marble fills. The musical notes C, F, A, C, heard in arpeggio, are things which possess real existence, but which are extended in time, and when we think of these separate sounds we lay them alongside each other in our mind in an empty, homogeneous medium which seems to be all that we think of as space. Yet the same notes heard simultaneously as a chord are not extended. They interpenetrate each other, but yet they are distinct things, since on hearing the chord we can recognise the notes composing it. As an arpeggio the notes are an extensive manifoldness, but as a chord they are an intensive manifoldness.

The mechanistic biology of the latter part of the nineteenth century based itself on the methods and concepts of physics, and it was therefore compelled to assume that the manifoldness of the “primitive” life-substance--the “Biophoridæ” of Weismann and his followers--or that of the fertilised ovum, was a manifoldness that had spatial extension. All the systems studied by physics were aggregates of elements, or parts, that had such extension: the sun, with its attendant planets and satellites, was a system of bodies isolated from each other in space. Even the atmosphere, or the sea, media which to our unaided senses appear to be homogeneous, are really media consisting of discrete bodies, or molecules, which are not actually in contact with each other, but which are separated from each other by empty space. Chemical compounds were assemblages of molecules, molecules were assemblages of atoms, and the atoms themselves were either simple or were composed of corpuscles, or still smaller bodies. This mode of analysis was forced upon the human mind by formal logic and geometry, and it was apparently the only method of acquiring mastery over nature. Yet there were difficulties, appreciated no less by the philosophical physicists than by the writers on formal philosophy. How could bodies, or molecules, or atoms that were separated from each other act upon each other? The molecule A could only act upon the molecule B if there were some particles between them which could convey the impulse or attraction, but then we must suppose that there were other particles between these intermediate ones, and so on ad infinitum, otherwise how could a body act, that is, really exist, where it was not? In other words, how could there be action at a distance? How, for instance, could the atoms of the earth attract those of the moon with a force sufficient to break a steel rope of 400 miles in diameter? Physics had therefore to invent the ether of space, not only to account for interstellar or interplanetary gravitation and other modes of radiant energy, but also to account for the interaction of the atoms or molecules which make up chemical compounds. In our own day atoms have ceased to be the limits to the subdivision of things: they are composed of electrons, but the electrons are entities separated from each other by empty space. They are not, however, the ultimate limits of subdivision of matter, as the atoms were supposed to be by the chemistry of the early part of the last century, but are regarded as “singularities” in an universal continuous medium or ether. It is of no moment that we are unable to describe the ether in terms of our former concepts of matter and energy, or at least that we can only so describe it in such a way that it is represented by negative qualities: we are compelled to postulate its existence in order to avoid philosophical confusion. The universe is therefore a continuum, and an atom or any other body exists wherever it can act. The atoms of a fixed star, so far away that we can only represent its distance in billions of miles, are nevertheless on our earth as well as at the point of space which we regard as their astronomical position, for the light emitted by them acts on our retinas. The universe is an unitary thing in that it is a continuous medium or substance in the philosophic sense, but it is also a multiplicity in that singularities or conditions of this medium pervade each other throughout space. Such seem to be the conclusions towards which the later physics forces us, and it is interesting to reflect how different biological speculation might have been had it been formulated now instead of half a century ago!

Why has a process of evolution occurred at all? Why is it that tendencies that might have co-existed, that indeed do co-exist to some extent, have become separate from each other? It is possible to conceive of an organism which contains chlorophyll, and which might therefore synthesise carbohydrate and proteid from inorganic substances, but which might also contain a sensori-motor system, and which might therefore expend the energy so obtained in regulated movements. To a certain extent such organisms combining the plant and animal modes of metabolism do exist among the Protista. Yet, the effect of the evolutionary process has been more and more to dissociate the plant and animal modes of metabolism until the typical animal is quite unable to make use of carbon dioxide and water as materials to be synthesised, while the typical plant has lost all power of motion except the tropistic movements of its roots, leaves, and stems. Instinctive and intelligent behaviour coexist in many animals, yet the tendency of man, most highly intelligent of all, is more and more to act intellectually; while the opposing tendency, that is, to act instinctively, has been evolved in the Hymenoptera. It seems as if such contrasting methods of transforming energy, or of acting, were incompatible with each other, and yet it is clear that they are not really incompatible, for they may co-exist. But it does seem clear that each of these contrasting tendencies cannot be manifested to the fullest extent if it is accompanied by the other. That is to say, life is limited in its power over inert matter. Manifested in the same material constellation, it cannot both use solar radiation to build up substances of high potential energy and then break down these substances so as to obtain kinetic energy of movement. Now we see clearly that life on our earth is indeed limited to a very restricted range of physical conditions. When we think of the mass of the earth we are surprised to find what an insignificant fraction of all this matter displays vital phenomena. The surface of the land is clothed with a layer of vegetation, luxuriant and abundant as we see it when we walk through a tropical forest, but which is really a film of inconceivable tenuity when we compare its thickness with the diameter of the globe. Even the whole surface of the land is not so clothed with vegetation, for polar regions and the tops of high mountains are almost lifeless, while desert tracts may be absolutely so. The lower strata of the atmosphere are inhabited by birds, insects, and bacteria, but the total mass of these is infinitesimal when compared with the total mass of the gases of which the atmosphere is composed. Even the sea, which we regard as rich in life, is not really so: estimates of the luxuriance of planktonic life are really misleading, for although a single drop of water may contain some hundreds of organisms, the mass of these is exceedingly small and is usually expressed as one or two parts per million. All this means that life has difficulty in manifesting itself in material forms. Whether it be simply a mode of interaction of some complex chemical substances with a relatively simple physico-chemical environment--the mechanistic view--or whether it be an impetus or agency which is neither physical nor chemical, but which acts through physical and chemical elements--the vitalistic view,--life is capable of acting on terrestrial materials to a very limited extent. Acting through all the tendencies which we see to exist in it, life may be, so to speak, diluted; but by being concentrated in one or a few of them it becomes more effective. The dissociation of this bundle of tendencies which we call life is therefore the meaning of the evolutionary process.

Ontogenetic development, says Roux, is the production of a visible manifoldness. It cannot be said that this cautious description of the developmental process has been apprehended by those who expound the dogmas of mechanistic biology. Development is indeed the production of a diversity, but this diversity is only a phase of a preceding diversity, a rearrangement of spatially extended pre-existing elements. How else could the developing embryo and its material environment be regarded as a system of physico-chemical elements, capable of study by the methods of experimental and mathematical physics, except by regarding it as a system passing through phases each of which is a necessary consequence of the preceding one, and each of which contained the same elements separated from each other in space? Let us think of water occupying a vessel at a high temperature and continually cooling. The states of this system are (1) the gaseous state in which the molecules of the water are moving at a high velocity and are a relatively considerable distance apart, and in which they are incessantly colliding with each other and with the walls of the vessel; (2) the state of the system consisting of the separate phases, liquid water and gaseous steam in contact with it; and (3) the solid phase, in which the molecular motions almost, or quite, cease. Here the progress of the system through its phases leads to physical diversity and then again to physical homogeneity. But the diversity of the different phases is in a sense an apparent one only: any single phase, or at least those which involve the passage of the system from the gaseous to the liquid phases, and vice versa, can be represented by van der Waal’s general equation, RT = (p + a/v^2) (v - b). Does anything in modern biological investigation, except, of course, the speculations of non-physical physiologists, suggest that an ontogenetic process can be represented in such a manner?

Are the arbitrary “stages” of the embryologists--the ovum, blastula, gastrula, etc., phases in a system in the above sense, the only sense in which the process can be regarded as capable of physico-chemical analysis? What precisely is the embryo at the close of the process of segmentation? It is an harmonious equipotential system, that is to say, an assemblage of discrete organic parts or cells, each of which has all the potentialities that every one of the others has. Any cell in the blastula may become a cell, or a series of such, in any part of the gastrula or pluteus larva. This is what the parts are in potentiality, but actually their individual fates are different. The system is an harmonious one, and each of its parts, although able to do whatever any other part can do, yet does one thing only: it becomes an endoderm cell, or an ectodermal cell, or a part of the skeleton, and so on; what it does depends on its position with regard to the other cells. An extensive manifoldness or diversity is produced, but this was not the consequence of a preceding extensive manifoldness, for in the preceding stage all the parts of the system were the same. The manifoldness of the ovum or blastula--that potential manifoldness which became actual in development--must be an intensive manifoldness, and admitting this we must abandon the comparison of the ontogenetic (and, of course, phylogenetic) processes with the phases of a physico-chemical system in process of transformation. Evolution is the transformation of an intensive into an extensive manifoldness.

More than this--much more than this--must be the difference between the transforming systems of physics and the evolving systems of biology. There is a quality, or sense, or direction in all naturally occurring inorganic processes which is not like that of organic evolutionary processes. We return now to the consideration of the second law of thermodynamics, for only in this way can we approach the notion of the vital impetus. If an energy-transformation occurs in inorganic nature, that is to say, if anything happens, the transformation occurs or the thing happens because there were diversities in the system in which it occurred. The condition for inorganic happening is that there must have been differences of energy in the different parts of the system: in the most general sense there must have been diversity of the elements. But with the transformation this diversity disappears, or tends to disappear, and it cannot be restored--that is, differences of energy cannot again be established unless by a compensatory energy-transformation; that is, energy must be expended on the system from without by some external agency. Whatever else physics shows us it shows us an unitary universe, that is, an universe in which anything that happens affects, to some extent, all the other parts. Therefore the diminution of diversities, or energy-differences, is something that cannot be undone, or compensated, for there is nothing without the universe. Everything that happens in our universe reduces the possibility of further happening. We desire, at the risk of reiteration, that this principle of energetics should be perfectly clear: inorganic happening, of whatever kind it may be, is a case or consequence of the second law of energetics--is the second law itself in a sense. All energy-transformations occur because energy-differences are being diminished, because diversities are being abolished. This is the sense, or quality, or direction of inorganic phenomena.

It is assumed that the universe is a finite one. If it were infinite the whole discussion becomes meaningless, and we must give up this and other problems.

It is not the direction of organic evolution. In the development of the individual organism what we most clearly see is the progressive increase of diversity of the parts. In phylogenetic evolution one, or a few, simple morphological forms of life have become, and are becoming, indefinitely numerous morphological forms. Diversity is continually increasing. If we cling to the mechanistic view of life, we must suppose that the diversity of the fully developed organism, or that of the organic world with all its species, was also the diversity of the fertilised ovum or that of the primitive life-substance in another phase. Then we commit ourselves to all the crudities of modern speculations on heredity.

With this increasing diversity of form there is a concomitant segregation of energy. We see as clearly as possible that the tendency of all inorganic happening is the transformation of potential into kinetic energy, and the equal distribution of this kinetic energy throughout all the parts of the system in which the happening occurred. On the other hand, the tendency of organic happening is the transformation of kinetic energy into potential energy, (1) in the stores of chemical compounds which result from the metabolism of the green plants, and which are capable of yielding energy again; and (2) in the results of the instinctive or intelligent activities of the animal’s organism. The first result of organic evolution is clearly to be traced and needs no further explanation, the second is apparent on reflection, but is perhaps not clearly apprehended in all its significance by the student of biology and physics.

Organic evolution is the process which has had, or is having, for its tendency the development of the putrefactive and fermentation bacteria, the chlorophyllian organisms, the Arthropods, and man and other mammals. All that we have said has been futile if this teleological description of the evolutionary process has not been clearly suggested. The indefinitely numerous forms of life that have appeared on the earth in the past, and are now appearing, seem to be experiments most of which have been unsuccessful. Only in the organisms mentioned, organisms which are complementary in their metabolic activities, has life been successful in manifesting itself in activities which are compensatory to those of inorganic nature. The energy which is dissipated in the radiation of the cooling sun is again made potential in the form of the carbohydrates, synthesised from water and carbon dioxide by the agency of the chlorophyllian organisms, and this energy accumulates. It is employed by the instinctive and intelligent animal, in that it is used as food and converted into bodily energy, which can then be utilised for any purpose that is contemplated. These plant substances taken in by the animal as sources of energy are broken down into excretory substances, which are further broken down by the metabolic activity of the fermentation and putrefaction bacteria, and become the substances used as foods by the chlorophyllian organisms.

If the activities of man were only those of undirected or misapplied muscular movements (as indeed most of his activities have so far been), then cosmic energy would truly be dissipated after it had become the energy of organisms. But does not all the history of man point to his ever-increasing activity in the conquest over nature, that is, the effort to hoard and employ natural sources of energy, and to arrest its tendency towards dissipation?

It must be admitted that the past history of human civilisation has been almost entirely that of the irresponsible exploitation of natural resources--for it has been founded on the thoughtless and wasteful utilisation of energy which was made potential by the plant and animal organisms of the past. Man, the hunter, maintained himself and multiplied by the destruction of other animals or plants, or by the mere collection and utilisation of naturally occurring fruits and other plant-substances. During historic times the bison and other animals have almost become extinct owing to his ruthless activity, just as in our own days the whale, sole, and turbot are disappearing before the activity of the machine-aided fisherman. Industrial man has been successful with his factories and railroads and steamships, and his electrical power and transport, only because he has been able to utilise the stores of energy contained in the coal and oil accumulated in the rocks of the earth. The progress of civilisation has been a progress rendered possible by discovery and invention, and by the application of the knowledge so obtained to the practical things of human life, but in this speculation and its application two different things are indicated. For the scientific man and the philosopher the reduction of the apparent chaos of nature to law and regularity is the beginning and end of his mental activity; but the object of the “entrepreneur” or “organiser” or the “captain of industry” has been to employ these results of thought to the irresponsible exploitation and the selfish depletion of natural sources of energy. Just as the bison and other animals have disappeared or are disappearing before the hunter and fisherman, so the stores of coal and oil are disappearing before the activities of commerce. It has been said that the triumphs of industrialism are only the triumphs of the scientific childhood of our race. Human effort has so far only contributed to the general dissipation of natural energy.

Yet just as man, the hunter, has been succeeded by man, the agriculturalist, so this irresponsible depletion of natural wealth must be succeeded by the endeavour to retard, and not to accelerate, the degradation of energy. Plants and animals which were simply killed by primitive man are now sown and harvested, or cultivated and bred; so that the energy of solar radiation, which formerly ran to waste, so to speak, is now being fixed by the metabolic activity of the green plants of our crops and harvests. Rainfall and winds, tides and rivers, all represent energy primarily derived from solar radiation and from the orbital and rotatory motions of the earth and moon. This energy even now is almost entirely dissipated as waste, irrecoverable, low-temperature heat; but more and more as our stores of coal and oil are being depleted, the attention of men is being directed to these sources of kinetic energy. Waterwheels and windmills, and the more effective mechanisms that must be evolved from these primitive motors, will capture this waste energy and convert it into the kinetic energy of machines serviceable to man, or into the potential energy of chemical compounds capable of storage and future utilisation. The study of radio-activity has made us acquainted with the enormous stores of potential energy locked up in the atoms, and if it ever should become possible to utilise this by the disintegration of these particles, the downward trend of natural energetic processes will further be retarded.

Life, when we regard it from the point of view of energetics, appears therefore as a tendency which is opposed to that which we see to be characteristic of inorganic processes. The direction of the latter is towards the conversion of potential into kinetic energy, and the equal distribution of the latter throughout all the parts of the universe. The direction of the tendency which we call life is towards the conversion of kinetic into potential energy, or towards the establishment and maintenance of differences of kinetic energy, whereby the latter remains available for the performance of work. In general terms, the effect of the movement which we call inorganic is towards the abolition of diversities, while that which we call life is towards the maintenance of diversities. They are movements which are opposite in their direction.

What is cosmic evolution? In all the hypotheses which astronomical physics has imagined we see the transformation of a system--a part of the universe arbitrarily detached from all the rest--through a series of stages, each phase of the series being marked by a progressive decrease of diversity, that is, by some degradation of energy. Two main series of hypotheses accounting for the present condition of the universe seem to have been the result of physical investigation: (1) the origin of discrete solar and planetary bodies by a process of condensation of a gaseous nebular substance; and (2) the origin of the same systems by aggregations of meteoric dust. Plausible as is the nebular hypothesis on first consideration, it fails when it is subjected to minute analysis. What is a gaseous nebula? It is a mass of heated vapour contracting by the mutual gravity of its parts as its molecules lose their heat by radiation--so the hypothesis states. But it has been pointed out that we cannot be certain that the gaseous nebulæ known to astronomy are hot, or even that they gravitate. The great nebula in Orion, it is stated, is at an enormous distance from us, and making a minimal estimate of this distance the volume of the nebula must still be incredibly great. There are good reasons for believing that the mass of the visible universe cannot be greater than that of a thousand million of suns such as our own. Assuming that all this matter is contained in the great nebula in Orion (and obviously only a small portion of it can be so contained), we find on calculation that the “gas” so formed would be much less dense than even the trace of gas contained in a high vacuum artificially produced. How, then, can we speak of such a body as this nebula as an extended mass of hot gas, cooling and gravitating as it loses heat?

Its density would be 1/(58 × 10^8)th that of our atmosphere.

Even on the other hypotheses, those of the formation of discrete suns and planets by the aggregation of meteoric dust, and the compensatory dispersal of such dust by radiation pressure, apparently insurmountable difficulties arise. All such hypotheses as we have indicated assume material substance and modes of energy-transformation similar to those that we study in laboratory processes, and all such hypotheses involve the notion of the degradation of energy. So long as we suppose that all cosmic processes are transformations of extended systems of material substances we must assume that energy is dissipated at every stage of the transformation, and whenever we assume this we admit that the processes are irreversible ones, and that the material universe as a whole tends towards a condition of inertia. Yet this, we see, cannot be true, for the universe teems with diversity. Is the progress towards the ultimate state of inertia an asymptotic one, as Ward suggests? This does not help us, since all that the suggestion does is to misapply a mathematical device of service only in the treatment of the problems for which it was developed. Somewhere or other, it has been said, the second law of thermodynamics must be evaded in our universe.

How can it be evaded? That movement or progress which we call inorganic is a movement of energy-transformations in one direction--towards their cessation. It is a movement which we can easily reverse in imagination. A cigarette consumed by a smoker represents the downfall of energy: the cellulose and oils of the tobacco burn with the liberation of heat, and the formation of water, carbon dioxide, and some soot; and this is what happens when potential energy contained in an organised substance becomes converted into kinetic energy. Now, the opposite process can clearly be conceived--it can even be pictured. If we make a kinematographic record of the smoking of the cigarette and then reverse the direction of motion of the film, we shall see the particles of soot recombining to form the substance of the cigarette, and we can imagine the concomitant combination of the water, carbon dioxide, and other substances formed during the combustion with the absorption of kinetic energy. This is not a mere analogy, for the same reversal of ordinary chemical happening occurs whenever a green plant builds up starch from the water and carbon dioxide of the atmosphere and it also occurs whenever a chemical synthesis of an “organic” compound, like that of urea by Wöhler, or that of the sugars by Fischer, is brought about in the laboratory. In all such syntheses the experimenter reverses the direction of inorganic chemical happening. He may cause endothermic chemical reactions, reactions accompanied by the absorption of available energy, to take place, and in these kinetic energy becomes transformed into potential energy. All the syntheses of organic compounds so complacently instanced by mechanistic biologists and chemists as indicative of the lack of distinction between the organic and the inorganic point to no such conclusion. Sugar is built up in the cells of the green plant from the inorganic compounds, water, and carbon dioxide, and is therefore a compound prepared by life--that of the plant organism. But sugar may also be built up in the laboratory from inorganic compounds, which may further have been synthesised by the chemist from their elements. Does this destroy the distinction between compounds formed by the agency of the organism and those formed by inorganic agencies? Obviously it does not, for in the green plant the sugar was formed as the result of the vital agency of the living chlorophyllian cell, while in the laboratory it was built up because of the intelligence of the experimenter. Apart from this intelligence or vital agency, the series of chemical transformations beginning with the elements carbon, oxygen, and hydrogen, and ending with the substance sugar, would not have occurred. We have no right to say, therefore, that such syntheses destroy the distinction between the organic and the inorganic. What they do indicate is the distinction between the tendency expressed by the second law of thermo-dynamics (inorganic processes), and those that occur as the result of direction conferred upon processes taken as a whole, either by the vital agency of the living cell, or by the intelligence of man (vital processes).

The direction, therefore, that may be conferred on a series of physico-chemical processes is what we must understand by the “vital impetus” of Bergson, or the “entelechy” of Driesch.

It must be admitted that it is difficult to describe more precisely than we have done above what is meant by these terms. It is with very much the same embarrassment that is experienced by the physicist when he has to apply the concepts of mass and inertia, in their eighteenth-century meaning, to his description of an universe in terms of electro-magnetic theory, that we seek to describe the modern concept of entelechy. Yet the physicist has had to make this step forward, and the same adventure awaits the biologist if the speculative side of his science is to make further progress, and if he is disinclined to make his science an appendage of physics and chemistry. Entelechy does not correspond to the eighteenth-century notion of a “vital force,” or to the “soul” of Descartes, as the writer of a book on evolutionary biology seems to suggest. It is a concept which is forced upon us mainly because of the failure of mechanistic hypotheses of the organism. If our physical analysis of the behaviour of the developing embryo, or the evolving race or stock, or the activities of the organism in the midst of an ever-changing environment, or even the reactions of the functioning gland, fail, then we seem to be forced to postulate an elemental agency in nature manifesting itself in the phenomena of the organism, but not in those of inorganic nature. This argument per ignorantium possesses little force to many minds: it makes little appeal to the thinker, or the critic, or the general reader, but it is almost impossible to over-estimate the appeal which it makes to the investigator, as his experience of the phenomena of the organism increases, and as he feels more and more the difficulty of describing in terms of the concepts of physics the activities of the living animal.

We may, however, attempt to illustrate mainly by analogy what is meant by Driesch’s entelechia, a more precise concept than is Bergson’s élan vital. We return to the consideration of the behaviour of the embryo at the close of the process of segmentation. The organism at this stage consists of a number of cells organically in continuity with each other, either by actual protoplasmic filaments or by the apposition of parts of their surfaces, thus constituting “semi-permeable” membranes. These cells are all similar to each other, both structurally and functionally. It does not matter that modern speculations on heredity describe them as unlike in that each contains a different part of the original germ-plasm which had been disintegrated in the process of the division of the ovum and the first few blastomeres; and it does not matter that these hypotheses are compelled to assume that a part of the original germ-plasm remains intact, being destined to form the gonads of the adult animal. These are hypotheses invented to account for the differentiation of the embryo in terms of eighteenth-century physics and chemistry, and they have yet to be supported by experiment before we can accept them as a description of what is to be observed in the processes of nuclear division and segmentation. Further, it is certainly the case that any one cell of the early embryo can give rise to any part of the larva. The segmented embryo is therefore a system of parts, all of which are potentially similar to each other. But actually each of these parts has a different fate in the process of the development of the larva, and this fate depends on what is the fate of the adjacent cells. There is also a plan or design in the development of the embryo--that is, a very definite structure results from this process--and each of the cells shares in the evolution of this design. The system of cells is therefore an harmonious equipotential system. The cells themselves are not the ultimate parts of this system, for each of them is an aggregate of a very great number of substances which are physico-chemically characterised--at least our methods of analysis seem to show that each cell is a mixture of a number of chemical compounds, but we must never forget that it is the dead cell which we thus subject to analysis, and not a living organism. Let us call these supposed chemical constituents of the living cells the elements of the system; then at the beginning of the process of development the latter is composed of elements which are not definitely arranged but which are distributed in an “homogeneous” manner very like the distribution which is effected on shuffling a pack of cards. But as differentiation proceeds, the elements of this system become unequally distributed, and the diversity becomes greater and greater, attaining its maximum when the definitive tissues and organs of the adult become established, just as at the close of a game of bridge the cards acquire a particular arrangement indicative of a very definite plan which was present in the minds of the players shortly after the game began.

Mechanistic biology would seek to explain this transformation of a homogeneous system of elements into a heterogeneous and specific arrangement by the interaction of the elements with each other, and by the reaction of the environment. But, given a homogeneous arrangement of elements capable of interacting with each other, then only one final phase can be supposed to be produced. A mixture of sulphur, carbon dust, copper and iron filings raised suddenly to a high temperature will only interact in one way, and the final phase of the system will depend on the composition of the mixture, on the temperature, and on the conduction of heat into the mixture in the initial stage of heating. A mixture of chloroform and water shaken up in a bottle is at first a “homogeneous” mixture of the particles of the two substances, but under the influence of gravity the liquids separate from each other and form two distinct layers, each of which will contain in solution some of the other liquid. A homogeneous mixture of different substances therefore becomes a heterogeneous arrangement in the inorganic system, as in the organic one, but while we can predict the former one we cannot predict the latter. We can express the result of the combination of the elements of the inorganic mixture as something that depends on chemical and physical potentials, but this is quite impossible in the case of the development of the embryonic system. It is not only that our knowledge of the developmental process is imperfect: the distinction between the two processes of differentiation is a fundamental one. A change in the conditions under which the inorganic system differentiates leads of necessity to a different final phase, but a change in the conditions under which the embryo develops need have no such effect. If some unforeseen occurrence takes place--some artificial interference with the process of segmentation, which could never have been experienced in the racial history of the organism--a regulation by the parts of the embryo occurs, and the final phase of development may be the same as if no interference had been experienced. That which is operating in the development of the embryo is something that is permitting, or suspending, or arranging physico-chemical reactions.

Let us think of the developing embryo merely as an aggregation of substances contained in an inorganic medium: the segmented frog’s egg floating on the water at the surface of a pond is an example. As an inorganic system its fate is determined. Autolysis of the substances in the cells will occur and the proteids will break down with the formation of amido-bodies, while other chemical changes, strictly predictable if our knowledge of organic chemistry were more complete than it is, would also occur. Putrefactive and fermentative bacteria will attack the proteids, fats, and carbohydrates, and in the end our aggregation of chemical substances will become an aggregation of much simpler compounds--water, carbon dioxide, marsh gas, sulphuretted hydrogen, phosphoretted hydrogen, ammonia, nitrates, etc., all of which will dissolve in the water of the pond, or will diffuse into the adjacent atmosphere. But in the living embryo this is not what occurs: an entirely different, and much more complex, arrangement of the chemical substances originally present in the segmented egg, or at least a physical and chemical re-arrangement, is brought about. The entelechy of the developing embryo prevents some reactions from occurring and directs the energy which is potential in the system towards the performance of other reactions.

Two analogies, suggested by Driesch, will perhaps make the rôle of entelechy more clear. A workman, a heap of bricks, some mortar, some food, and some oxygen constitute a system in the physico-chemical sense. From his heap of bricks and mortar the workman may build one of several different kinds of small house, or he may perhaps construct several walls without any definite arrangement, or he may merely convert one “disorderly” heap of bricks and mortar into another “disorderly” heap. In the same way a man, a case of movable types, some food, and some oxygen constitute another system. The initial phase of this system consists of the compositor, his food, and some fifty-odd boxes of types, each of which contains a large number of similar elements. A final phase of the system may be the arrangement of the types to form an epic poem, or a series of dramatic criticisms, or a meaningless jumble of correctly spelt words. In all these cases the same amount of energy was expended: the bricklayer used up the same quantity of food and oxygen and excreted the same quantities of water, carbon dioxide, and urea, whether he made a house, or a small chimney, or a heap of bricks without architectural arrangement. The system of bricks and mortar acquired during the process of differentiation a gradually increasing complexity; while in the case of the type-setting the diversity of arrangement acquired in the final phases may be of a very high order. Yet the intelligent mind of the worker remained in either case unchanged.

Let us consider further a man walking along the ties, or sleepers, of a railway track. The ties are at variable distances apart, so that the steps of the walker must vary in length, being sometimes closer together, sometimes further apart. The mean step has a definite length and requires the expenditure of a certain amount of energy, and the condition that the man takes sometimes a long step and sometimes a short one does not require that the energy expended on the steps should be more than if every one of them were of the mean length, for the additional energy that is required for the long steps is saved from the short ones. That which operates here is the power of regulation exercised by the walker regarded as a mechanism. There is no purely inorganic process precisely similar to this. It might be thought that the governor of a steam engine did very much the same thing, admitting more steam into the cylinder when the load on the engine increases, and vice versa. But the governor is a mechanism designed to compensate for variations that are given in advance. In the case of the man walking on the railway track, entelechy operates by suspending energetic happening (the muscular contractions of the short steps) when necessary, and allowing it to proceed when necessary. Entelechy itself, whatever it may be, need not be affected by these regulations.

The organism is therefore an aggregation of chemical substances arranged in a typical manner. These substances possess energy in the potential form, capable of undergoing transformation so that they may give rise to other chemical substances--secretions, for instance--or to energy in the kinetic form, that is, the movements of muscles. In the resting organism these transformations do not take place: the energy remains potential, so that chemical happening is suspended. In the unfertilised ovum, for instance, nothing happens although all the potentialities of segmentation are contained in the cell. If reactions did occur in consequence of the chemical potentials contained in the substances of the cells, the progress of these would be such as to lead to the formation of substances in which potential energy was minimal, and in which the original energy of the cell would be represented by the un-co-ordinated kinetic energy of the molecules resulting from the breakdown of the substances undergoing the chemical changes. This is not what happens in the differentiation of the ovum: the developing cell forms new substances from those of its inorganic medium similar to the substances of which it is already composed, and then these substances become arranged to produce the specific form of the organism into which the ovum is about to develop.

All hypotheses which attempt to describe the functioning of the differentiating ovum, or the functioning organism, in terms of the physical concepts of matter and energy alone, fail on being subjected to close analysis. The manifestations of the life of the organism are, it is said, particular “energy-forms,” of the same order as light, heat, chemical and electrical energy, etc. All these energy-forms are “concatenated,” that is, each can be converted into any of the others. A particular frequency of the vibration of the ether can be converted into a movement of the molecules of a material body, and so become heat, while chemical energy may become converted into electrical energy, or vice versa, and so on. It is said that life may be merely a transformation of some “energy-form” known to us: the potential energy of food may be converted into “biotic energy,” and this may then manifest itself in the characteristic behaviour of the organism. This is the method of physical science. Energy continually disappears from our knowledge: the mechanical energy which was employed to carry a weight to the top of a hill, or that which raises a pendulum to the highest point of its swing, apparently disappears. If we pass a current of electricity through water, energy disappears, for it requires more current to pass through water than through a piece of metal of the same section. In these and similar cases physics invents potential energies in order to preserve the validity of the law of conservation. The kinetic energy of the weight, or that of the swinging pendulum, becomes the potential energy of the weight resting at the top of the hill, or that of the bob of the pendulum at its highest point, while the electrical energy that has apparently been lost becomes the potential energy of the changed positions of the molecules of oxygen and hydrogen. This assumption that the visible kinetic energy of motion becomes converted into the invisible potential energy of position is justified by our experience, for (neglecting dissipation) we can recover this lost energy, in its original quantity, from the condition of the bodies which became changed physically when the kinetic energy disappeared. Apply the same method to the phenomena of the organism and suppose that the chemical potential energy of the food consumed becomes converted into the kinetic energy of motion of the parts of the body: we are justified in this assumption by the results of physiology. But then some of this chemical energy undergoes a transformation of quite another kind and becomes the “biotic energy,” which is apparently that which is in us which enables us to perform regulations, or establishes that condition which we call consciousness. We cannot say exactly what this “biotic energy” is, or what are the steps by which the energy of food becomes converted into it; but no more can we say what is electrical energy, nor what are the steps by which chemical energy becomes converted into it. Thus our ignorance of the precise nature of the energy-transformations of inorganic things--an ignorance which is all the while disappearing--becomes the excuse for a comparison of these with vital transformations, and for the assumption that there is a fundamental similarity in the two kinds of happening.

Less is assumed in the assumption of an entelechian agency than in assuming that the manifestations of life are the consequences of a vital “energy-form,” different from inorganic forms, though belonging to the same order, inasmuch as it may be concatenated with these inorganic energy-forms. We need not suppose that a particular kind of transformation occurs only in the sphere of the organic: all that we need assume is that, by some agency inherent in the activities of the organism, chemical reactions that would occur if the constellation of parts were an inorganic one are suspended. Nothing unfamiliar to physical science is involved in this assumption. Hydrogen and chlorine, gases that combine together when mixed with the production of heat and light, may be mixed under conditions such that the combination may be delayed for an indefinite time. Iron which dissolves in nitric acid may nevertheless be brought into the “passive” form when it remains in contact with the re-agent but is not dissolved by it. Enzymes which are in contact with the walls of the alimentary canal do not dissolve these membranes so long as the tissues are alive, and they do not dissolve the food stuff until they have been “activated.” Oxygen which is contained in the tissues does not oxidise the tissue substances until an enzyme or a catalase has exerted its influence. More and more, as physiology has become more searching in its study of the functions of the animal, has it sought to explain the metabolic processes by assuming the intervention of enzymes, until the number of these substances has become legion, and much of the original simplicity of the notion of ferment-activity has been lost. But why do not these enzymes, if they are always present in the tissues, always act? They must be activated, says modern physiology; that is, the enzyme really exists in the tissues as a “zymogen” or a substance which is not, but which may become, an enzyme; or they exist as “zymoids,” that is, substances which appear to be chemically enzymes, but which must be activated by “kinases” before they can become functional.

Undoubtedly it is along these lines that physiology is making advances, has increased our knowledge of the activities of the animal, and is conferring on the physician greater power of combating disease; but the hypotheses of the activity of the enzymes is obviously one which has been based on the results of the physico-chemical investigation of inorganic reactions, and it has taken the precise form it has because of the attempted analogy of many metabolic processes with catalytic processes. Why do the inert zymoids become activated by the kinases just when they are required by the general economy of the whole organism? We do know that kinases are produced by the entrance of digested food into certain parts of the alimentary canal, and that these kinases are carried in the blood stream to other parts where they activate the zymoids already there. But of the nature of the machinery by means of which all this is effected physiology gives us no hint, and it is an assumption that the mechanism involved is a purely physico-chemical one. Suppose we say that the entelechy of the organism possesses the power of suspending the activation of the enzyme, that is to say, of arresting the drop of chemical potential involved in the process of the hydrolysis of (say) a proteid. When this process of hydrolysis is necessary in the interest of the organism entelechy can then institute the reaction which it has itself suspended: all this is in accord with the law of conservation. Entelechy does not cause chemical reactions to occur which are “impossible”: it could not, for instance, cause sulphuric acid and an alkaline phosphate to react with the formation of hydrochloric acid. But chemical reactions which are possible may be suspended, and suspended reactions may then become actual when this is necessary in the interest of the organism.

Entelechy is therefore not energy, nor any particular form of energy-transformation, and in its operations energy is neither used nor dissipated. In all that it does the law of conservation holds with all the rigidity with which we imagine it to hold in purely inorganic happening--at least we need not assume that it does not hold--and this is the essential difference between the entelechian manifestations and the manifestations of the “vital” or “biotic” forces or energies of the historic systems of vitalism. It is essentially arrangement, or order of happening, and it is therefore a non-energetic agency. The workman who may build half-a-dozen zigzag walls, or an archway, or a small house, from the same materials and with the expenditure of the same quantity of energy, is indeed an energetical agent, but he is more than that. He is a physico-chemical system in which any one phase is not determined by the preceding phase. Different results may arise from the same initial arrangement of materials and energies, and this is because the system contains more than the material and energetical elements. It contains the intelligence or entelechy of the workman.

What is this entelechy? Sooner of later in all our speculation on organic happening we must cross the arbitrary line which divides the space of our concepts from the non-spatial--the intensive from the extensive. Just as the physicists have left materiality behind them in their speculations and treatment of the phenomena of radiation, so biology must attempt to trace back the materiality of the organism to something which is immaterial. Just as physics has now abandoned the idea of matter as something which consists of discrete particles, or atoms, having extension in space, and which therefore exclude each other, so biology must seek the origin of living things, not in the hypothetical “biophoridæ,” or other ultimate living material particles, but in the intensive manifoldness of entelechy. There is a manifoldness in the potentiality which the simple and homogeneous ovum possesses of becoming the heterogeneous adult organism. This manifoldness, says the mechanistic biologist, consists of a manifoldness of extended material units, the determinants of Weismann, and the organisation that arranges these units--what is this organisation? It cannot be a three-dimensional machinery, as all close analysis of the facts of development and regulation shows. It is then something that is intensive, something which is not in space, but which acts into space, and the result of which is manifested in spatial material arrangements and activities. Vague and incomprehensible as is this concept of the activities of the organisms, it is only vague and incomprehensible because we have been accustomed to express all chemical and physical happening in terms of the fundamental concepts of matter and energy, and the science of the last two centuries has left us with a terminology which applies strictly to operations in which only these concepts are involved. But if, as all minute analysis of vital phenomena shows, the search for the antecedents of some energetic, material, extended system of elements in a preceding energetical, material, extended system of elements only leads to confusion and contradictions, then this concept of an agency which is neither energetic, nor material, nor spatial must be formulated. Entelechy, then, is not energy, but rather the arrangement and co-ordination of energetic processes. It is not something that is extended in space, but something which acts into space. It is not material, but it manifests itself in material changes. It is a manifoldness, or organisation, but the manifoldness is an intensive one. Compare this definition with the notion of the ether of space now accepted by the mathematical physicists, and it will be seen that our speculations are similar to those of the physicists, and, like them, the test of their reality and usefulness is to be justified pragmatically.

* * * * *

We may now attempt a formal description of the organism based on the discussions of the previous chapters.

This description is largely an expansion of Driesch’s “Analytical definition of the individual living organism.” The reader should note also that it includes the Bergsonian idea of duration, and that of the organism as a typical phase in an evolutionary flux, as parts of the description.

The organism is a typical constellation of physico-chemical parts or elements.

That is to say, it is an object in nature possessing a definite form, which is the result of the arrangement of its tissues. Each tissue is again an arrangement of cells, and each cell is a complex of chemical substances. The organism therefore resembles, so far as our definition goes, an inorganic crystal. But it is the typical organism that we are considering, and this is a pure conception, for our typical organism does not occur in nature. The organisms that are accessible to our observation are constellations of physico-chemical parts, but these constellations tend continually to deviate from the conceptual arrangement. Progressive variation from the type is something that distinguishes the organic constellation from the inorganic one.

The organism is an entity in which energy-transformations of a particular nature are effected. These transformations raise energy from a state of low, to a state of high potential.

This is the general tendency of terrestrial life, and it is expressed most fully in the metabolism of the green plant. The energy-transformations that are effected here are those in which the kinetic energy of radiation is employed to build up chemical compounds of high potential, from inorganic substances incapable in themselves of undergoing further transformations. The general tendency of all inorganic transformations is towards inertia. In them energy is not destroyed, but it is dissipated: it becomes uniformly distributed throughout material bodies as the un-co-ordinated motions of the molecules of which those bodies are composed, and it ceases to be available for further transformations. The green plant reverses this transformation, and accumulates energy in the form of chemical compounds of high potential. Inorganic processes are those in which available energy becomes unavailable, and this unavailable energy can only become available again if a compensatory energy-transformation is effected. Life is that which effects these compensatory energy-transformations.

The organism is a constellation capable of indefinite growth by dissociation.

That is to say, it is a constellation which reproduces itself in all its specificity. Growth consists in the separation from the organism of a part, or reproductive cell, which divides (or dissociates) repeatedly, each dissociated part growing again in mass by the addition of substances similar to its own, but which are taken from a medium dissimilar in composition to itself. The aggregate of parts so formed then differentiates so that the constellation is reproduced in all its specificity. There is nothing precisely similar to this in inorganic happening. The growth of a crystal consists simply of the accretion of elements similar in nature to those of the growing body, and there is no differentiation.

The organism exhibits autonomy.

It is a constellation which persists in the midst of an ever-changing environment, and the typical organic form remains the same, although the material of which it is composed undergoes continual change. There are inorganic entities which resemble the organism in this respect: the form of a cyclone or atmospheric disturbance, for instance, remains the same even though the air of which it is composed is continually changed. But the form of the organism does not vary strictly with the changes in the environment in which it is placed, for it may respond to an environmental change by a regulation, or compensatory change in form or functioning, the effect of which is to maintain the constellation in all its specificity. The regulation is not a complete or perfect one, for environmental changes do, to some extent, produce changes in the organic constellation, but there is no functionality between the environmental change and the organic response. In inorganic happening a change in one part of a transforming system necessarily determines the nature and extent of the changes that occur in the other parts of the system.

The organism is a centre of continuous action.

It is first of all a part of nature in which energy-transformations continually take place--a description which applies equally well to plants and animals. It is only when we attempt to seek an inorganic system to which this definition would apply that we find how well it differentiates the organic from the inorganic. An inorganic system which transforms energy is either one which tends continually towards stability, or it is a machine made by man for a definite purpose, and it is therefore a system involving a teleological idea. An organic centre of action is one in which energy-transformations proceed without cessation.

In the plant organism the energy-transformations represent, with the exception of the reproductive processes, the whole activity of the organism. In the animal organism they are accessory to regulated and purposeful motile activity, that is, muscular action. The object of this muscular activity varies with the stage of evolution attained by the animal. Its sole object in the lower animal is that of individual or racial preservation. Living in an organic and inorganic environment which is always hostile and tends continually towards its destruction, the whole activity of the organism is directed to the attempt to master this environment: it struggles for its individual existence, and that of its offspring. The activities of man are also these, but they are more than these, for, knowing that physical processes tend continually towards inertia, he seeks to control these processes, and to preserve the instability of nature on which the possibility of further becoming depends.

The activity of the organism, whether it be the energy-transformations of the plant or the motile activities of the animal, are directed and regulated activities. The activity of the organism is not a functional activity in the sense that the activity of a dynamo is a function of the nature of the machine, and of the nature and quantity of the energy supplied to it. The nature of the activity of the organism is regulated autonomously by purposes which it “wills” to carry out.

The organism is a phase in an evolutionary flux.

Categories of organisms--varieties, species, genera, etc.--are fictions. They are arbitrary definitions designed to facilitate our description of nature. They are types or ideas. In constructing them we follow the method of the intellect, and we represent by immobility that which is essentially mobile and flows. Between the fertilised egg and the senile organism there is absolute continuity. Our description of the individual organism is a description of it at a typical moment of its life-history, and this description includes all that has led up to, as well as all that will fall away from, the morphology at this particular typical moment.

Even then the arbitrarily defined organism is only a phase. In defining it we arrest, not only the individual, but also the racial, evolutionary flux. The specific morphology is that of a typical moment in a racial flux. Leading up to it at this moment are all the variations that have joined it with its ancestry, and leading away from it will be all the variations that will convert it into its descendants.

The individual and racial developments are true evolutions. They are the unfolding of an organisation which was not expressed in a system of material particles or elements interacting with each other, and with the elements of the environment, but which we must seek in an intensive, non-spatial manifoldness.

In the evolutionary flux the changes are non-functional ones, that is to say, any phase, whether it be one in an individual or a racial development, is not merely a rearrangement of the elements of the preceding phases, as in the case of a transforming system of material particles and energies. There is inherent, spontaneous variability.

The organism endures.

That is, all its activities persist and become part of its organisation. It does not matter whether or not we decide that characters which are acquired are transmitted, nor does it matter whether or not we conclude that the environment is the cause of these acquirements. Some time or other in the individual or racial history new characters arise by the activity of the organism itself, and these characters either persist in an individual or in a race. They endure. All its activities, even its thoughts, persist and form the experience of the animal--an experience which continually modifies its conduct. In man those true acquirements, the results of education and of investigation, persist as written language, or as tradition, even if they are not inherited.

Duration is not time. The mathematician does not employ, in his investigations, intervals of duration. When he relates something which is happening now to something which happened some time ago he employs the differential co-efficient dy/dx, so that the interval between the two occurrences becomes an “infinitesimal” one. When the astronomer predicts events that will happen some years hence, or describes those that happened some years ago, he is really describing things that are all there at once, so to speak, things which are given. If we unfold a fan, stick by stick, we see the separate members in succession, but they are all there, and we can, if we like, see them all at once.

The more we reflect on it the more we see that mathematical time is only a way in which we see things apart from each other. Things become extended in time as they become extended in space. Whether occurrences capable of analysis by the methods of physics are what we call past or future occurrences, they are all given, in that each of them is only a phase of the others.

Duration belongs to the organism. The past is known because all that has occurred to the organism still persists in its organisation. The future is unknown because it has still to be made. Duration is therefore a vector--something having direction, and the organism progresses out of the past into the future. It grows older but not younger.

* * * * *

Such appears to be the nature of life. Can we discuss the problem of its origin?

Did life originate on our earth? We must first consider what we mean when we speak of an origin. The organic world of the present moment, with all its environment--that is to say, the totality of organisms on the earth, with all the materials which they can utilise in any way, the energy of radiation from which they ultimately derive their energy, and all the parts of the cosmos which interact with them--constitute a system in the physical sense. The present condition of the organic world, that is, the kinds and numbers of organisms, and their distribution, and the distribution of the materials which they can utilise, and the quantity and nature of the energy which is available to them, are the present phase of this system. All the conditions of life in the past, that is to say, the kinds, and numbers, and distribution of organisms, and the quantity and nature of their environment at any time, together formed phases of this system. If there was a time when life, as we know it, did not exist, then the materials and the energies, which were antecedent to life when it did appear, were also a phase of the system. On a strictly mechanistic hypothesis there could be no origin: there could only be a transformation of a system which was already in existence. All that exists to-day was given then. When, therefore, we speak of the origin of life from non-living materials we mean simply a transformation of those materials and energies.

There was a time, it is said, when life could not exist on the earth. For the organism is essentially that aggregate of chemical compounds which we call protoplasm, and this cannot exist at temperatures higher than 100° C., and it cannot function at temperatures lower than 0° C. It requires carbon dioxide, and ammonia or nitrate, as the materials for its constructive metabolism, and there was a time when these compounds could not exist, for they must have been dissociated by the heat of the gaseous nebula from which our earth originated. The organism requires energy in the form of solar radiation of a particular frequency of vibration, and there was a time when the sun’s radiation was different from what it is now. Therefore life did not exist then. Even if we believe that life came to the earth as germs, which existed previously in outer cosmic space, this belief does not solve the problem, which simply becomes transferred from our earth to some other cosmic body.

But life, as we know it, makes use of the materials and the energies which are available to it in the conditions in which it exists. The plant organism obtains its energy from solar radiation because this is the most abundant source of terrestrial energy. The human eye is most susceptible to light of a particular frequency of wave-length, but this is the radiation that is most abundant in the light of the sun. Does this not mean that the organism has merely adapted itself to the material and energetic conditions in which it exists? Does it necessarily mean that because the conditions were very different life could not exist? Protoplasm could not exist at a temperature of several thousand degrees Centigrade, but does that mean that life, which on any hypothesis of mechanism must be described in terms of energy, could not exist in these conditions?

It must have had an origin, says Weismann, because it has an end. Organic things are destroyed, inasmuch as they disintegrate into inorganic things. Organisms die. Thus the organic process comes to an end, and because it comes to an end it must have a beginning. Spontaneous generation of life is thus, for Weismann, a “logical necessity.”

Need this logical necessity exist? The argument clearly implies that life is a reversible process. Organic things become inorganic, and therefore inorganic things must become organic things. The first statement is a fact of our experience, but the second one would only be logically true if we were to postulate that the process of life, whatever it may be, is a reversible process. But we must not postulate this if we are to hold to a physico-chemical mechanism, for it is a fundamental result of physical investigation that all inorganic processes are irreversible: reversible inorganic processes are only the limits to irreversible ones. Physical processes go only in one way, and that organic substance is destroyed to the extent that it becomes inorganic is a particular case of this irreversible physical tendency. Now the mechanism of Weismann must base itself on the concepts of physics and chemistry, and it must postulate the origin of life from non-living substances. Why? Because life is a reversible process, that is, it exhibits a tendency which does not exist in inorganic processes. Clearly the logic is faulty! And must we conclude that life has an end? Weismann himself suggests that nothing in the results of biology indicates that physical death is a necessity: it is rather an adaptation. The soma, or body, is the envelope of the germ-plasm, and exposed as it is to the vicissitudes of an environment which is always hostile, it becomes at length an unfit envelope. But with the reproductive act the germ-plasm acquires a new soma, and it is no longer necessary that the former one should continue to exist as an unfit envelope. Physical death therefore occurs as an adaptation serving for the best interests of the race. The organism need not die, for the germ-plasm may be a physical continuum throughout innumerable generations. Somatic death is only a destructive metabolism: it is a catastrophic metabolism, if we like.

We may legitimately discuss such problems as the origin of the protoplasm of the prototrophic organism, or that of the chlorophyll-containing cell, or that of the nerve-cell. On the mechanistic view each of these conditions is a phase of a transforming physico-chemical system, and it is within the scope of the methods of physical science to investigate the nature of these transformations. But if the argument of this book is sound, then the problem of the origin of life, as it is usually stated, is only a pseudo-problem; we may as usefully discuss the origin of the second law of thermo-dynamics! If life is not only energy but also the direction and co-ordination of energies; if it is a tendency of the same order, but of a different direction, from the tendency of inorganic processes, all that biology can usefully do is to inquire into the manner in which this tendency is manifested in material things and energy-transformations. But the tendency itself is something elemental.

APPENDIX

MATHEMATICAL AND PHYSICAL NOTIONS

It must be understood that some of the things dealt with in these appendices are very hard to understand by the reader acquainted only with the results of biological science. We urge, however, that they are all relevant if biological results are to be employed speculatively.

INFINITY

What is really meant when the mathematician uses the concept of infinity in his operations? Suppose that we take a line of finite length and divide it into halves, and then divide each half into halves, and so on ad infinitum. We make cuts in the line, and these cuts have no magnitude, so that the sum of the lengths into which we divide the line is equal to the length of the undivided line. We can divide the line into as many parts as we choose, that is, into an “infinite” number of parts.

Suppose that we are making a thing which is to match another thing, and suppose that we can make the thing as great as we choose. If, then, no matter how great we make the thing, it is still too small, the thing that we are trying to match is infinitely great.

Substitute “small” for “great,” and this is also a definition of the infinitely small.

Clearly the idea of infinity does not reside in the results of an operation, but in its tendency. It inheres in our intuition of striving towards something, but not in the results of our striving.

FUNCTIONALITY

If we pour some mercury into a U-tube closed at one end, the air in this end will be contained in a closed vessel under pressure. We can increase the pressure by pouring more mercury into the open end of the tube. We can measure the volume of the air by measuring the length of the tube which it occupies. We can measure the pressure on this air by measuring the difference of length of the mercury in the two limbs of the tube. By taking all necessary precautions we shall find that for each value which the pressure attains there is a corresponding value of the volume of the air.

We thus find the pressure values, p↓{1}, p↓{2}, p↓{3}, p↓{4}, p↓{5}, etc., and the corresponding volumes, v↓{1}, v↓{2}, v↓{3}, v↓{4}, v↓{5}, etc., and we may then plot these values so as to make a graph.

In this figure the values represented along the horizontal axis are pressure-values, and those represented along the vertical axis are volume-values. We have so made the experiment that we can make the pressure-values whatever we choose--let us call them the values of the independent variable or argument. For each value of the pressure, or argument, there is a corresponding value of the volume, which depends on the pressure--let us call these values of the volume values of the dependent variable or function.

We can make arbitrary values of the pressure, but whenever we do this the corresponding values of the volume are fixed. We say, then, that the volume is a function of the pressure. In general, when we choose one value of an independent variable, or argument, there can be only one, or a small number, of values of the dependent variable, or function. If there are two or more values of the function for one value of the argument each of these is necessarily determined by the value which we choose to assign to the argument. There is a strict functionality between the two series of variables. In the experiment we have chosen this functionality is expressed by the equation pv = k(1 + at), where p is the pressure, v the volume, k and a constants, and t is the temperature at which the experiment is carried out. In a number of experiments like that which we have mentioned, k, a, and t are the same throughout, and this is why we call them constants. We give p any value we like, and then v can be calculated from the equation.

RATE OF VARIATION

If we know the equation pv = k(1 + at), we can find how much the volume changes when the pressure changes, that is, the rate of variation of v with respect to p. But even if we don’t know that this equation applies, we can still find the rate of variation from our experiments. We see from the graph that, when the pressure increases from p↓{1} to p↓{2}, the volume decreases from v↓{1} to v↓{2} but that if the pressure is again increased to p↓{3}, that is, by a similar amount to the increase of pressure from p↓{1} to p↓{2}, the volume decreases from v↓{2} to v↓{3}. Now we find, by measurements made on the graph, that the decrease v↓{1} to v↓{2} is greater than the decrease v↓{2} to v↓{3}, and the latter decrease is greater again than the decrease from v↓{3} to v↓{4}. Evidently the rate of variation of volume is not like the rate of variation of pressure, that is, the same throughout, and when we look at the graph we see that the rate of variation is greatest where the slope of the curve is steepest. The latter is steepest near the point a, less steep near the point b, and still less steep near the point c. Now any small part of the curve is indistinguishable from a straight line. Let us draw a straight line ee↓{1}, which appears to coincide with a small part of the curve near a, and similar straight lines ff↓{1}, and gg↓{1}, which also appear to coincide with small parts of the curve near b and c. Then the steepness of the curve will be proportional to the angles which these straight lines make with the axis op, and these angles are measured by their tangents, that is, by the ratio oe↓{1}/oe, which is the tangent that e↓{1}e makes with op, the ratio of↓{1}/of, and the ratio og↓{1}/og.

The point a on the curve corresponds with a pressure a↓{1} and a volume a↓{11}. The point b corresponds with a pressure b↓{1} and a volume b↓{11}, and c with a pressure c↓{1} and a volume c↓{11}. The average rate of variation of the volume of the gas, as the pressure changes from a to c, is therefore proportional to the sum of the tangents oe↓{1}/oe and og↓{1}/og, divided by 2.

THE NOTION OF THE LIMIT

Suppose that we wish to find the rate of variation of volume for a pressure change in the immediate vicinity of the value b↓{1}, that is, the rate of variation as the pressure changes from a little less than b↓{1} to a little more than b↓{1}. If we find the point b on the curve corresponding to b↓{1}, and if we then draw a line ff↓{1}, touching the curve at the point b, we shall obtain the angle off↓{1}. It might appear now that the tangent of this angle, that is, the ratio of↓{1}/of, would give us a measure of the rate of variation of volume.

But the reasoning would be faulty. The line ff↓{1} only touches the curve, it does not coincide with an element of the curve. Also at the point b↓{1} the pressure has a certain definite value, and there is no change. At the corresponding point b↓{11} the volume also has a certain definite value, and there is no change. There can therefore be no rate of variation. The value of the tangent does not give us a measure of the rate of variation: it gives us the limit to the rate of variation, when the pressure is changing in the immediate vicinity of b↓{1}.

We must stick to the notion of a pressure change in the immediate vicinity of b↓{1}. What do we mean by “immediate vicinity”? We mean that we are thinking of a range of pressure-values in which the particular pressure-value b↓{1} is contained, but not as an end-point. We mean also that we choose a definite standard of approximation to the value b↓{1}, so that any pressure-value within our interval differs from b↓{1} by less than this standard of approximation. It means further that, no matter how small is the number representing this standard of approximation, any pressure-value within the interval will differ from b↓{1} by less than this number. This is what we really mean when we say that the interval we are thinking about is an “infinitely small one.”

Now corresponding to this interval of pressure-values in the immediate vicinity of b↓{1}, there will be an interval of volume-values in the immediate vicinity of b↓{11}, and, as before, any one of these volume-values will differ from b↓{11} by less than any number representing a standard of approximation to b↓{11}. We then find the point on the curve corresponding to both b↓{1} and b↓{11}, that is b, and we draw the line ff↓{1}, and find the tangent of the angle which this line makes with op. The value of this tangent is the limit of the rate of variation of the volume of the gas when the pressure undergoes a change in the immediate vicinity of b↓{1}.

“Rate of variation” is a function of the argument “pressure.” This function has the limit l for a value of its argument b↓{1}, when, as the argument varies in the immediate vicinity of b↓{1}, the value of the function approximates to l within any standard whatever of approximation.

If the reader does not understand this, he should read Whitehead’s “Introduction to Mathematics.” He should read this book in any case.

We should not, of course, find the rate of variation of volume of the gas by this means. We should calculate the value of the differential co-efficient dv/dp from the equation pv = k(1 + at): this would be k (1 + at)/p^2. But the reasoning involved in the methods of the calculus are those which we have attempted to outline. We try to avoid the terms “infinitely small,” “infinitely near,” “infinitely small quantities,” and so on, by the device of standards of approximation. It may appear to the non-mathematical reader that all this is rather to be regarded as “quibbling,” but the success of the methods of mathematical physics should convince him that such is not the case. He should also reflect that clear and definite ideas on the fundamental concepts of the science are just as necessary in speculative biology as they are in mathematics.

(Another example.)

Let us consider the case of a stone failing from a state of rest. Observations will show that when the stone has fallen for one second it has traversed a space of 16 feet; at the end of two seconds it has fallen through 64 feet; and at the end of three seconds the space traversed is 144 feet. From these and similar data we can deduce the velocity of motion of the stone as it passes any point in its path.

The velocity is the space traversed in a certain time s/t. If we take any easily observable space (say five feet) on either side of the point chosen, and then determine the times when the stone was at the extremities of this interval, and divide the interval of space by the interval of time, we shall obtain the average velocity of motion of the stone over this fraction of the whole path chosen. But the velocity did not vary in a constant manner during this interval (as we see by considering the spaces traversed during the first three seconds of the fall). Therefore our average velocity does not accurately represent the velocity of the stone as it passes the point at the middle of the path chosen.

We therefore reduce the length of the path more and more so as to make the average velocity approximate closer and closer to the velocity near the middle portion of the path. In this way we find the ratio δs/δt, where δs is a very small interval of path containing the point chosen, but not as an end-point, and δt is a very small interval of time. Perhaps this average velocity may be near enough for our purposes, but perhaps it may not. The interval of path δs is still a finite interval, and δt is still a finite time, and so long as these values are finite ones the velocity deduced from them remains a mean one. All that we can say is that it approximates to the velocity, as the arbitrary point was passed, within a certain standard of approximation.

Obviously the smaller the interval δs, the closer will be this approximation. Suppose, then, that we diminish δs till it “becomes zero.” It might appear now that when δs coincides with the point chosen we shall obtain the velocity of the stone at this point. But if there is no interval of path, and no interval of time, there can be no velocity, which is an interval of path divided by an interval of time; and if the stone is “at the point,” it does not move at all. We must stick to the idea of intervals of space and time, and yet we must think of these intervals as being so small that no error whatever is involved in regarding the mean velocity deduced from them as the “true velocity.” We therefore think of the point as being placed in an interval of path, but not at an end-point of this interval. We think of the velocity as a mean one, but we must have a standard of approximation, so that we may be able to say that the mean velocity approximates to the “actual” or limiting velocity of the stone as it passes the point, within this standard of approximation. The smaller we make the interval, the closer will the mean velocity approximate to the limiting velocity.

We therefore think of the stone as moving in the immediate vicinity of the point in the sense already discussed. We say that the “immediate vicinity” is an interval such that any point in it, p↓{1}, approximates to the arbitrary point p which we are considering within any standard of approximation: that is, no point in the interval is further away from p than a certain number expressing the standard of approximation, and this can be any number, however small. We say the same thing about the interval of time. That is to say, we make the intervals as small as we like: they can be smaller than any interval which will cause an error in our deduced velocity, no matter how small this error may be.

The limit of the velocity of a stone falling past a point in its path is, therefore, that velocity towards which the mean velocities approximate within any standard of approximation, when we regard the interval of space as being the immediate vicinity of the point, and the interval of time as being the time in the immediate vicinity of the moment when the stone passes the point. The limit of the velocity is not δs/δt but ds/dt, dt and ds being, not finite intervals of time and space, but “differentials.” We determine this limit by the methods of the differential calculus.

FREQUENCY DISTRIBUTIONS AND PROBABILITY

Let the reader keep a note of the number of trumps held by himself and partner in a large number of games of whist (the cards being cut for trump). In 200 hands he may get such results as the following:

No. of trumps in his own and partner’s hands--0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

No. of times this hand was held--0, 0, 0, 1, 9, 29, 53, 52, 35, 14, 6, 1, 0, 0.

He should note also the number of times that trumps were spades, clubs, diamonds, and hearts: he will get some such results as the following: spades, 46; clubs, 53; diamonds, 51; hearts, 50.

The numbers in the lower line of the first series form a “frequency distribution,” for they tell us the frequency of occurrence of the hands indicated in the numbers above them. “No. of trumps” is the independent variable, and “no. of times these nos. of trumps were held” is the dependent variable.

A frequency distribution represents the way in which the results of a series of experiments differ from the mean result. A particular result is expected from the operation of one, or a few, main causes. But a number of other relatively unimportant causes lead to the deviation of a number of results from this mean or characteristic one. Yet since one, or a few, main causes are predominant, the majority of the results of the experiment will approximate closely to the mean; and a relatively small proportion will deviate to variable distances on either side of the mean. If a pack of cards were shuffled so that all the suits were thoroughly mixed among each other, then we should expect the trumps to be as equally divided as possible between the four players. But a number of causes lead to irregularities in this desired uniform distribution, and so the results of a large number of deals deviate from the mean result. It is possible, by an application of the theory of probability, to calculate ideal, or theoretical frequency distributions, basing our reasoning on the considerations suggested above. We then find that the observed and calculated frequency distributions may be very much alike.

In biological investigation, far more than in physical investigation, we deal with mean results. It is, however, just as important that the mean should be considered as the individual divergences from the mean. We want to know the mean results, and the way and the extent in which the individual results diverge from the mean.

There is a mean or “ideal” result, but we must think of a great number of small independent causes which cause the actually obtained results to diverge from this mean. If these small un-co-ordinated causes are just as likely to cause the results to be less than the mean, as greater than the mean, we shall obtain a frequency distribution resembling the one given above, in that the variations from the mean are equal on both sides of the mean. But if the general tendency of the small un-co-ordinated causes is to cause the results, on the whole, to tend to be greater than the mean, then the frequency distribution will be “one-sided,” that is, if we represent it by a curve the latter will be an asymmetrical one. Curves which are asymmetrical are those most frequently obtained in biological, statistical investigations.

MATTER

Our generalised notion of matter is that it is the physical substance underlying phenomena. Immediately, or intuitively, we attain the notion of matter because of our perceptions of touch, and our perception of muscular exertion. The distance sense-receptors, visual, auditory, and olfactory, would not give us this intuition of matter.

Material things are extended, that is, they have form, and they exclude each other, so that they cannot occupy the same place. They appear to us to be aggregates of different nature: they may be solid and homogeneous, like a piece of metal; or solid and porous, like a piece of pumice-stone; or loose and granular, like sand; or viscous or liquid, like pitch or water. They may have colour. They are opaque, or transparent in various degrees. They may have odour. Material things, as they are perceived by the distance sense-receptors, appear to have qualities.

Material things are aggregates of molecules. The aggregates may possess essential form, like that of a crystal, or an organism. The form of the aggregate may be essential and homogeneous, so that it consists of molecules, all of which are of the same kind, like a crystal. It may be heterogeneous and essential, like the body of the organism, when it consists of molecules which are not all of the same kind. The aggregates may have accidental form, like that of a river valley, or a delta, or a mountain, and the form in these, and similar cases, is not a part of the essential nature of the aggregate.

The molecules are selections (in the mathematical sense) of some of about eighty different kinds of atoms. A molecule is a small number of atoms arranged together in a definite way, and its nature depends, not only on the kinds of atoms of which it is composed, but also on the arrangement of these atoms. Two or more different arrangements of the same atoms are, in general, different molecules.

MASS

When matter is perceived by the tactile and muscular sense organs, we have the intuition of mass. It is heavy, and the degree of heaviness is proportional to the quantity of matter in the body which we feel, that is, to its mass. Heaviness is synonymous with weight, but weight does not depend alone on the quantity of matter in the body. If the latter were removed to an infinite distance from the earth or other cosmic bodies, its weight would disappear, but its mass would remain. We could still touch and move it, and we should still find that different degrees of muscular exertion would be necessary when bodies of different masses had to be moved.

INERTIA

If the body were in motion, we should find that muscular exertion is necessary in order that it might be brought to rest; and if it were at rest, we should find that muscular exertion was necessary in order that it might be moved. The body, matter in general, possesses inertia, and this is its most fundamental attribute. Mass we can only conceive in terms of inertia. If two bodies were at rest, and if the same degree of muscular exertion conferred on each the same initial velocity of motion, their masses would be equal. If the same degree of muscular exertion conferred different velocities on different bodies, their masses would be different, and would vary directly with the initial velocities conferred.

FORCE

The feeling which we experience when we move a body from a state of rest, or stop a body which is moving, is what we call force. If on climbing a stair in the dark we think there is one step more than there is, and so have the queer, familiar, feeling of treading on nothing, we have the intuition of energy; but when we tread on the steps, and so raise our body, we have the intuition of force. Force is that which accelerates the velocity of a mass. If the latter is at rest, we consider it to have zero velocity. If it is moving, and we stop it, there is still acceleration, but this is negative.

Matter, that is, the substantia physica, is clearly to be conceived only in terms of energy. It is, to our direct intuitions, resistance, or inertia, that which requires energy in order that it may be made to undergo change. Our static idea of physical solidity, or massiveness, disappears on ultimate analysis. Molecules are made up of atoms, and the atoms are assumed to have all the characters of matter: we could not see them, of course, even if we possessed all the magnifying power that we wished, for they would be too small to reflect light. Modern physical theory is compelled to regard atoms as complex, and imagines them as being composed of moving electrons. The electron is immaterial--it is the unit-charge of electricity. It is said to possess mass, but mass is now understood to mean inertia. So long as the electron is moving, it sets up a field of energy round it, and this field--the electro-magnetic one--extends in all directions. Periodic disturbances in it constitute radiation, and this radiation travels with the velocity of light. It is because of the existence of this field that we are obliged to postulate the existence of an ether of space. Unfamiliar to us until the discovery of Hertzian waves and “wireless” telegraphy, this electro-magnetic radiation in space is now accessible to our direct intuitions. We can initiate it by setting electrons in motion, that is, by expending energy (producing the sparking in the transmitters of the wireless telegraphy apparatus); and we can stop it, if it is in existence, by absorbing the energy (in the receivers of the wireless telegraphy apparatus). This is essentially what we understand by the inertia of gross matter. We set a body in motion by expending energy on it (the explosion of the powder in a cartridge, which converts potential chemical energy into the kinetic energy of the moving projectile); and we can stop a body which is in motion by absorbing this energy of motion (by causing the projectile to strike against a target, when the kinetic energy of its motion becomes the kinetic energy of the heat of the arrested body).

Inertia is therefore the same thing whether it be the inertia of visible, material bodies, or the inertia of invisible, material molecules, or the inertia of the immaterial, non-tangible ether. It is the condition that energy-changes must occur if anything accessible to our observation is to change its state of rest or motion.

ENERGY

Energy is therefore indefinable. It is an elemental aspect of our experience.

Nature to us is an aggregate of particles in motion. We have to speak of massive particles, whether we call these visible material bodies, or molecules, or atoms, or electrons, in order that we may describe nature. We must employ the fiction of a substantia physica. We only know the substance or matter in terms of energy; it is really the latter that is known to us. It is the poverty of our language, or rather it is the legacy of a materialistic age, that compels us to speak of particles that move, rather than of motions as entities in themselves.

Considering, then, the idea of particles in motion as a fiction necessary for clear description, we can study energy. There is only one kind, or form, of energy which presents itself to our aided or unaided intuitions, that is kinetic energy. Bodies that move possess this energy represented by their motion: they can be made to do work, that is, their energy can be transformed into other forms of energy. All things are in motion. A gas consists of molecules incessantly moving with high velocity, and colliding and rebounding from each other. The energy of a gas is the sum of one-half of the masses of all the molecules, multiplied by the squares of the velocities of all the molecules, that is, Σ1/2mv^2. This is also the kinetic energy of a projectile, or of a planet revolving round the sun. Kinetic energy is that of the uniform, unchanging motion of some entity possessing mass, but we must extend our notion of mass so as to include immaterial, imponderable entities such as electrons.

This energy cannot be destroyed or created--the law of conservation of energy. This is a principle or mode of our thought. We are unable scientifically or philosophically to think of an entity ceasing to be. Dreams and phantoms show us entities which are real while they last, but which cease to exist. If we do attempt to think of entities that appear from, or disappear into, nothing, we surrender the notion of reality. The more we think of it the more clearly we shall see that the things which we call real are the things which are conserved.

Yet energy, to our immediate intuitions, seems to disappear. A flying bullet strikes against a target and becomes flattened out into a motionless piece of lead. A red-hot piece of iron cools down to the temperature of its surroundings. A golf-ball driven up the side of a hill comes to rest in the grass. A current of electricity passing through water is used up, that is, electricity of a higher potential is required to force the current through water than to force it through thick copper wire. In all these cases we might think that energy is lost, but we cannot believe this. The kinetic energy of the flying bullet becomes transformed into the increase of the kinetic energy of the molecules of the metal of which the bullet was composed; for the latter becomes greatly heated when its flight is arrested and this increased heat ought to be equal to the kinetic energy of the bullet in flight. The red-hot piece of iron cools, and the kinetic energy of its molecules becomes less and less, but this does not cease to exist, for the energy is simply transferred by radiation and conduction to the surrounding bodies, the temperature of which it raises. The golf-ball driven up the hill comes to rest and loses its kinetic energy. Some of this has been transferred to the air through which it passes, the latter being heated very slightly; some of it is expended by friction with the grass over which the ball rolls before coming to rest, and this energy is traceable in heat-effects, or in mechanical effects, but the rest of it apparently ceases to exist. But this would be contradictory to the principle of conservation, and so we say that the lost kinetic energy has become potential. The current of electricity may heat the water through which it passes, and some of the energy which seems to disappear is so to be traced, but the greater fraction is apparently lost. A quantity of free hydrogen and oxygen is, however, generated, and we say that the kinetic energy of the moving electrons has become transformed into the potential chemical energy of the gaseous mixture.

POTENTIAL ENERGY

Therefore, if energy disappears or appears, we do not say that it is destroyed or is created: we invent potential energies, into which we suppose that the energies in question have become transformed, in order that we may still think of them as being subject to an a priori principle of conservation. Although a particle of radium continually generates heat, we do not therefore think of the first principle of energetics as being invalidated, for we suppose that the energy which thus appears was really potential in the atoms of radium. But it was contrary to all our former experience of atoms that they should contain any other energy than that of their own motion, and so the further assumption was made that the atom, at least the atom of the radio-active substance, is really complex, and not simple, as chemical theory demands. It is made up of smaller particles, and possesses a definite structure. In certain circumstances the atom may disintegrate, and the energy which held together its particles, whether these were simpler corpuscles or electrons, is given off as the heat which the radio-active substance apparently generates. The potential energy of the chemical atom is therefore a hypothesis which has been devised in order to preserve the validity of the law of conservation, and the reality of this hypothesis is being tested by investigation. If we accept it as true, are the deductions made from it justified in our experience? That is the test which must be satisfied in all the hypotheses where potential energies are invented, and the potentials are only real if the test is satisfactory. The golf ball at rest at the top of the hill is a different entity from the golf ball at rest at the bottom of the hill: it is capable of developing energy, for a touch may cause it to roll down the hill, when most of the energy which was expended in order to drive it to the top of the hill will reappear in the form of the kinetic energy of motion of the ball. The atoms of hydrogen and oxygen which were dissociated by the energy of the electric current are different things from the atoms of hydrogen and oxygen which are combined together to form the molecules of water. Their state when the gases are in the elementary condition, or are “free,” is that of molecules moving rapidly and incessantly, rebounding from each other after colliding with each other: they possess energy of position--potential energy--because they are separate from each other. If they “combine,” as when a minute electric spark explodes the mixture of gases, they tractate together, and remain in proximity to each other, becoming molecules of water. The energy which became potential in the gaseous mixture, when the electric energy of the current seemed to disappear, now appears as the heat generated by the combustion, that is, as the greatly increased kinetic energy of the molecules of the gas (steam) which takes the place of the mixture of hydrogen and oxygen. Previous to the explosion this gas was a mixture of molecules of hydrogen and oxygen (2H↓{2} + 2O) at the ordinary temperature, but after the explosion it consists of a smaller number of molecules at a very much higher temperature.

What is “energy of position”? The golf ball at the bottom of the hill was at a distance of R feet from the centre of the earth, but at the top of the hill it is at a distance of R + 100 feet from the centre of the earth. In the first case it was free to fall R feet, but in the second case it is free to fall R + 100 feet. The atoms of the constituent molecules of water occupy the position H - O - H, the bonds (-) indicating that the atoms are very close together; but when the water is decomposed by an electric current, the atoms occupy the positions O - O + H - H + H - H, the (+) indicating that the atoms are relatively far apart from each other. Now the golf ball and the earth, or the atoms of hydrogen and oxygen, are physically the same material entities, whether they are close together or far apart, yet when the earth and the ball, or the atoms of oxygen and hydrogen, are separated from each other, their “properties” are different from what they are when they are close together. What is it that makes the difference? It is that which is between them. Is it, in the last case, “the potential energy of chemical affinity”? This dreadful phrase is actually used in a recent book on biology: “In the elements carbon and oxygen, so long as they remain separate, a certain amount of energy remains latent. When the carbon and oxygen atoms are allowed to come together and unite, this potential energy of chemical affinity is liberated as kinetic energy.” What is changed by the tractation and pellation (the terms suggested by Soddy in place of the anthropomorphic ones, “attraction” and “repulsion”)? It is the ether which has become changed in some way. Potential energy resides therefore in the ether of space.

ISOTHERMAL AND ADIABATIC CHANGES

Let us consider the changes which occur in a gas under the influence of changes in temperature and pressure, premising that the remarks which we have to make can be applied to bodies in the liquid and solid conditions, with some necessary modifications. A gas, then, consists of a very great number of particles, or molecules, in motion. These molecules move in straight lines at very high velocities, and if the envelope in which the gas is contained is a restricted one, the molecules collide with each other, and with the walls of the envelope; and, being assumed perfectly elastic, they rebound from each other, and from the walls of the vessel, with the same velocity which they had when they collided. The pressure of the gas (say that of steam at a temperature of 110° C., and a pressure of 120 lbs. to the square inch in a steam boiler) is the sum of the impacts of the molecules on the walls of the containing vessel. When the temperature is high the molecules are moving at a higher mean velocity than when the temperature is lower, and their mean free path tends to become greater. The volume of a certain mass of gas, that is, the volume occupied by a certain very great number of molecules, is greater the higher is the temperature, provided the envelope is one capable of yielding. If we reduce the capacity of the envelope in which the gas is contained, the pressure will rise, for the intrinsic energy of the gas is still the same; but we have done work on it, and by the law of conservation this work, or at least the energy represented by it, must still exist. It is represented by the decreased length of free path of the molecules, and this means that the impacts on the walls of the vessel will be greater than they were. There is, therefore, a certain relation between the volume of a gas and its pressure, and this relation can be represented by an equation involving the temperature, the pressure, and the volume.

The diagram represents the pressure and the volume of a gas when these things change. There are two conditions, (1) when the heat developed by the compression is allowed to escape through the walls of the vessel to the outside, or when the heat lost in the expansion of the gas is compensated by the conduction of heat through the walls of the vessel from outside; and (2) when the heat developed is retained in the gas, as when the latter is contained in a vessel the walls of which do not conduct heat. The pressure of the gas is measured along the horizontal axis, and the volume is measured along the vertical axis, and a curve is drawn so that for any value of the pressure there is a corresponding value of the volume. Thus the values of the pressures p and p↓{1} in the diagram correspond to the value of the volume v. The curve relating the change of pressure with a corresponding change of volume is, in general, that called a rectangular hyperbola. But there are two kinds of such curves: (1) that which we obtain by plotting the corresponding values of pressure and volume, when the temperature of the gas remains constant throughout the series of changes, that is, when the rise of temperature which would occur when the gas is compressed is compensated by the conduction of this heat to the outside of the vessel containing the gas. Such a series of changes of pressure and volume is called an isothermal one. (2) When the heat developed by the compression of the gas is retained in the gas, as when the walls of the vessel in which these changes are effected are such as do not conduct heat: such a series of changes is called an adiabatic one. Adiabatic curves are steeper than are isothermal ones.

THE CARNOT ENGINE

This is an imaginary mechanism which performs a certain cycle of operations. It does not really exist, but the conception of its operation is of the greatest value in the consideration of energy-transformations, and it is for this reason that we discuss it here.

Consider a gas, or some other substance capable of expanding or contracting. It contains intrinsic energy, and it is capable of doing work. Thus, since a gas can expand indefinitely it can be made to do mechanical work. A mass of gas at a pressure p↓{1}, and having a volume v↓{1}, and at a temperature T°, can do work by expanding till its pressure is reduced to p, and its volume increased to v. If it expands adiabatically its temperature will fall to t°. Let us suppose that t° is the temperature of the surrounding medium: the gas cannot therefore cool further, and we can obtain no more work from it. If the gas is the substance which we wish to employ as the working substance in the Carnot engine, we must therefore bring it back to the condition represented by A. That is, we must raise its temperature to T°, we must reduce its volume to v↓{1}, and we must increase its pressure to p↓{1}.

Thus the steam of an engine is (say) at a temperature of 110° C., and a pressure of 120 lbs. to the square inch. When it has passed through the cylinder and condenser it is water at a temperature of, say, 15° C., and it is at atmospheric pressure. We must, therefore, bring it back to its former condition by heating this water in the boiler till it is steam under the former conditions of temperature and pressure.

Therefore we must, in order to obtain a self-acting engine, cause the working substance, and the mechanism of the engine, to perform a series of cyclical operations.

The Carnot engine is a cylinder containing a gas called the working substance S, and this gas can be brought into thermal contact with a source of heat, or a refrigerator, that is, the gas can be heated or cooled by a mechanism outside itself. The walls of the cylinder are made of some substance which is a perfect non-conductor of heat, but the bottom of the cylinder is made of a substance which conducts heat perfectly. There is a piston in the cylinder which fits it closely, but which moves up and down without friction. At the bottom of the latter is a valve which can be turned so as to place the bottom of the cylinder, and therefore the gas, in thermal contact with a reservoir of heat (+), or a refrigerator (-). But when the valve is turned so that the non-conducting part O fills the bottom, the gas is perfectly insulated, and heat can neither enter nor leave it.

Such an engine is, of course, an imaginary one, since there can be no mechanism in which there is not a certain amount of friction between moving parts, and there are no substances which conduct or insulate heat perfectly. The engine is, in fact, the limit to a series of engines each of which is supposed to be more perfect than the last one. It is a fiction which is of considerable use in theoretical work.

THE CARNOT POSITIVE CYCLE

We have therefore a substance which can be heated by contact with a hot body, and which can then expand, doing mechanical work by raising a piston, and perhaps turning a flywheel, and on which work is then done so that it returns to its original condition. This is a cycle of operations. If we consider only the changes which occur in the working substance we can represent these changes by a diagram.

First operation, (1→2). We suppose that the valve is turned so that the non-conducting plug closes the cylinder. The piston is in the position II (Fig. 31). Heat cannot then enter or leave the gas. But the latter already contains heat: it is at a temperature of T↓{2}°, so that it can expand doing work. Let it expand, forcing up the piston. During this operation the pressure of the gas will fall from a point on the vertical axis opposite 1 to a point opposite 2, and its volume will increase from a point on the horizontal axis beneath 1 to a point beneath 2. It will cool because it has expanded, and no heat is allowed to enter it during this act of expansion. The expansion is therefore adiabatic; the temperature falls from T↓{2}° to T↓{1}°; and work is done by the gas.

Second operation, (2→3). The piston is now at the position I, that is, at the upper end of its stroke, and we must bring it back again to the lower end of the cylinder. The valve is turned so that the bottom of the cylinder is placed in thermal communication with the refrigerator (-), and the piston is pushed in to the position II. The gas is therefore compressed until its volume decreases from a point beneath 2 to a point beneath 3. As it is being compressed, heat is generated and its temperature would rise, but as this heat is generated it flows into the refrigerator, so that the temperature of the gas remains the same during the operation. The contraction is therefore an isothermal one; the temperature remains at T↓{1}°; and work is done on the gas from outside.

Third operation, (3→4). But the piston is not at the lower end of its stroke yet. We turn the valve so that the bottom of the cylinder is closed by the non-conducting plug O, and then push in the piston until it reaches the position III. The gas is still further compressed, and this compression generates heat. But the heat cannot escape, so that the temperature of the gas rises until it reaches T↓{2}°. The contraction is therefore an adiabatic one. Work is done on the gas.

Fourth operation, (4→1). The piston is now at the lower end of its stroke. We turn the valve so that the bottom of the cylinder is placed in communication with the source of heat (+). The gas expands from the point beneath 4 to the point beneath 1, raising the piston to the position II. This expansion of the gas would lower its temperature, but it is in communication with the source of heat, and so it does not cool, but draws heat from the source and remains at a constant temperature, T↓{2}°. The expansion is therefore an isothermal one. Work is done by the gas.

This completes the cycle. But the gas is heated, and when the piston is at position II, the valve is turned so as to close the cylinder by the non-conducting plug O. The heat already contained in the gas continues to expand, the latter doing more work, but this expansion causes the temperature to fall from T↓{2}° to T↓{1}°. This is the operation with which the cycle commenced.

Summarising the positive Carnot cycle, we see that the engine takes heat from a source (+) and gives up part of this to a refrigerator (-), (in an actual steam-engine heat is taken from the boiler and given up to the condenser water). If we measure the quantity of heat taken from the boiler in the steam which enters the cylinders we shall find that this quantity of heat is greater than the quantity which is given up to the condenser water. What becomes of the balance? It is converted into the mechanical work of the engine. The Carnot engine therefore takes a quantity of heat, Q↓{2}, from the source and gives up another quantity of heat, Q↓{1}, to the refrigerator. We find that Q↓{2} is greater than Q↓{1} and the balance, Q↓{2} - Q↓{1}, is represented by the work done by the engine. Heat-energy falls from a state of high, to a state of low potential, and is partly transformed into mechanical work.

THE CARNOT NEGATIVE CYCLE

This is simply the positive cycle reversed. The reader should puzzle it out for himself if he is not already familiar with it. It consists of an adiabatic contraction 2→1, an isothermal contraction 1→4, an adiabatic expansion 4→3, and an isothermal expansion 3→2. A quantity of heat, Q↓{1}, is taken from the refrigerator at a temperature T↓{1}°, and another quantity, Q↓{2}, is given up to the source at a temperature T↓{2}°. But Q↓{2} is greater than Q↓{1}, and the engine therefore gives up more heat than it receives, while, further, heat flows from a body at a low temperature to another body at a higher temperature. Where does the engine get this energy from? It gets it because work is done upon it by means of an outside agency, and all of this work is converted into heat.

REVERSIBILITY

The Carnot engine and cycle are therefore perfectly reversible. Not only can the engine turn heat into work, but it can turn work into heat. This perfect, quantitative reversibility is, however, a property of the imaginary mechanism only, and it does not exist in any actual engine.

ENTROPY

Let us consider the cycle more closely. In the operation 4→1, which is an isothermal expansion, there is a flow of heat-energy from the source and a transformation of energy into work. The gas in the condition represented by the point 4 had a certain pressure and a certain volume. In the condition represented by the point 1, its pressure has decreased, its volume has increased, and its temperature is the same. Its physical condition has been changed, and to bring it back into its former condition something must be done to it. Let, then, the gas continue to expand without receiving any more heat, or parting with any: that is, let it undergo the adiabatic expansion 1→2 until its temperature falls to that of the refrigerator, T↓{1}°. We now compress the gas while keeping it at this temperature, that is, we cause it to undergo the isothermal contraction 2→3, during which operation it is giving up heat to the refrigerator, so that there is again a flow of heat-energy. We then compress it still further without allowing heat to escape from it, that is, we cause it to undergo the adiabatic contraction 3→4. During this operation the gas rises in temperature to T↓{2}°. It is now in the condition that it was when the cycle commenced.

In this cycle of operations heat first entered, and then left the gas, and with this entrance or rejection of heat, the condition of the gas with respect to its power of doing work changed. We investigate this flow of heat, and the concomitant change of properties of the substance, with regard to which the flow took place, by forming the concept called entropy. We make the convention that when heat enters a substance the entropy of the latter increases, and when heat leaves it its entropy decreases. We call the quantity of heat entering or leaving a substance Q, and the temperature of the substance T. Then Q/T is proportional to the change of entropy of the substance when the quantity of heat, Q, enters or leaves it.

Now it is a fact of our experience that heat can only flow, of itself, from a hotter to a colder body. Consider two such bodies forming an isolated system, the temperature of the hotter one being T↓{2}°, and that of the colder one T↓{1}°. Let Q units of heat flow from the body at T↓{2}° to that at T↓{1}° no work being done.

Then the loss of entropy of the hotter body is Q/T↓{2}°, and the gain of entropy of the colder body is Q/T↓{1}°. The nett change of entropy of the system is Q/T↓{1}° - Q/T↓{2}°. Since T↓{2}° is greater than T↓{1}°, Q/T↓{2}° is less than Q/T↓{1}°. Therefore the expression Q/T↓{1}° - Q/T↓{2}° is positive, that is, the entropy of the system, as a whole, has increased. When heat flows from a hotter to a colder body the nett entropy of the two bodies, therefore, increases.

But we can also cause heat to flow from a colder to a hotter body by effecting a compensatory energy-transformation. Such a compensation would not occur by itself in any system capable of effecting an energy-transformation, if it is to be effected some external agency must act on the transforming system. We can suppose it to happen in a perfectly reversible imaginary mechanism. Suppose a Carnot engine works in the positive direction, taking heat from a reservoir at temperature T↓{2}°, and giving up part of this heat to a refrigerator at T↓{1}°, and doing a certain amount of work W. Suppose that this work is stored up, so to speak, say by raising a heavy weight, which can then fall and actuate the same Carnot engine in the opposite (negative) direction. The engine then exactly reverses its former series of operations. The work it did is reconverted into heat, and as much of this heat flows from the refrigerator into the source, that is, from a colder to a hotter body, in the negative operations, as flowed from the source to the refrigerator in the positive operations. In this primary energy-transformation, combined with a compensatory energy-transformation, there is no change of entropy. The mechanism is an ideal one--the limit to an irreversible mechanism.

But--and now we appeal to experience and cease to work with ideal mechanisms--the actual engine which we can design and work is one in which there will be friction, in which some parts will conduct heat imperfectly, and other parts will insulate heat imperfectly. Let the friction generate q units of heat, and let the quantity of heat which is “wasted” by imperfect conduction and insulation be q↓{1}. This heat will flow into the refrigerator, or will be radiated or conducted to the surrounding medium, which we suppose to be at the same temperature as the refrigerator. If, then, we divide this total quantity of heat by the temperature T↓{1}°, we get (q + q↓{1})/T↓{1}° = S↓{1} as the quantity of entropy which is generated as the result of the imperfections of the engine, in addition to the quantity of entropy, S, which would be generated if the engine were a perfect one. Both S and S↓{1}_ are positive.

Also in the working of the engine in the negative direction a certain quantity of entropy, S↓{1}, is generated for reasons similar to those mentioned above.

The entropy generated when the engine works in the positive direction is therefore S + S↓{1}, and when it works negatively the quantity generated is also S↓{1}. The entropy destroyed when the engine works negatively is S. The total change of entropy is therefore 2S↓{1} + S - S, that is, 2S↓{1}. In an actual energy-transformation combined with a compensatory energy-transformation there is therefore an increase of entropy.

We can generalise these statements so that they will apply not only to a heat-engine but to all mechanisms which effect energy-transformations. In all such transformations entropy is generated. Therefore the Entropy of the Universe tends to a maximum.

AVAILABLE AND UNAVAILABLE ENERGY

Consider the Carnot engine as a perfect mechanism. It takes heat-energy from a source at a temperature T↓{2}°, and it gives up heat to a refrigerator at a temperature T↓{1}°, T↓{2}° being greater than T↓{1}°. In the adiabatic expansion 1→2 the gas continues to expand until its temperature becomes equal to that of the refrigerator. It cannot, then, expand and do work any longer, and thus the proportion of the heat, Q↓{2}, received from the source, which can be converted into work, depends on the difference of temperature T↓{2}° - T↓{1}°. The greater is this difference the greater will be the proportion of the heat-energy received which can be converted into work. If the engine were a perfect one, and if the gas were also a perfect one (that is a gas which would continue to expand according to the equation for the adiabatic expansion of gases), and if the refrigerator were absolutely cold, then all_ the heat energy received from the source could be converted into work.

We cannot produce a refrigerator of absolute temperature 0°, and therefore only a certain proportion of the heat which is received by the engine can be transformed into mechanical work. But this work can be used to reverse the action of the engine, and thus the same fraction of the total heat-energy which was given to the refrigerator can be taken from it and given back to the source. The perfect engine is therefore reversible without loss of available energy.

Now consider still the engine as a mechanism which takes heat from a source and gives it to a refrigerator, but let it be an actual engine. Instead of giving up a certain fraction of the heat received to the refrigerator--a fraction equal to Q↓{1} (T↓{1}°/T↓{2}°), it gives up rather more, because it is not a perfect mechanism, that is, it generates friction, etc. Some of the heat received thus ceases to be available for the performance of work; and passes into the refrigerator. The fraction of the heat-energy which passes into the refrigerator in the perfectly reversible engine was unavailable energy in the conditions in which the mechanism worked, or was imagined to work, but in the actual engine this fraction is increased. If we divide the increase of unavailable energy by the temperature of the refrigerator, the product is the increase of entropy generated in the actual engine over that generated in the ideal engine. Because of this reduction of available energy the actual engine is an irreversible mechanism.

This is the connection between unavailable energy and entropy. In all transformations some fraction of the transforming energy becomes heat, and this heat flows by conduction and radiation into the surrounding bodies. In general this heat simply raises the temperature of the medium into which it flows, and becomes unavailable for further transformations. With every transformation that occurs some part of the energy involved becomes unavailable. Therefore although the sum of the available and unavailable energy of the Universe remains constant, the fraction of unavailable energy tends continually to a maximum.

INERT MATTER

We can see now what is indicated by Bergson’s “inert matter.” It is not matter deprived of energy--such an expression has no meaning--it is energy which is unavailable for further transformations.

The matter in which we choose to say that this energy is inherent has become inert. Let us substitute for the Carnot engine the actual steam-engine of a ship, the condenser of which is cooled by the sea water which is taken in, and which is then heated and flows out again into the sea. The heat derived from the source, that is, from the furnace of the boiler where coal is burned to raise steam, thus passes out into the sea. Now the heat capacity of the sea is so great that the temperature of the water is not appreciably raised by this heat, which drains into it from the engine: even if it were appreciably raised, the heat would be conducted into the earth, or would be radiated out into space, and would then raise the temperature of the material bodies of the universe. But let all this heat remain in the sea. It then simply raises the temperature of the water by an exceedingly small amount, and the motions of the molecules become infinitesimally increased. But the heat becomes equally distributed by conduction and convection throughout the mass of the water in the sea, and as there are no differences in adjacent parts there are no means whereby the energy which thus passes into the sea can be again transformed.

A new order of things is the result of the processes we have indicated. The segregated, available heat-energy of material bodies has become transferred to the un-co-ordinated, diffuse, unavailable energies of the molecules which compose these bodies. The transformations which we can effect depend on the condition that the energy which we utilise is that of aggregates of molecules which are in a different physical condition, as regards this energy, from adjacent aggregates. But when this energy becomes equally distributed among the molecules of all the aggregates, the matter in which it inheres becomes inert. If we could, by a sorting process like that of Maxwell’s hypothetical demons, a process which does not expend the energy with which it deals, separate the molecules which were moving slowly from those which were moving more quickly, we could make this energy again available. But it must clearly be understood that our physics is the physics not of individual molecules, but of aggregates of molecules.

INDEX

Absolute, Driesch’s theory of, 47.

Acceleration (in physics), 355.

Acquired characters induced by the environment, 216; a means of transformism, 220; evidence of transmission scanty, 225; transmission not inconceivable, 226.

Actions, categories of, and consciousness, 282; deliberative, 283; mechanistic hypothesis of, 157; stereotyped, 283; at a distance, 304.

Activation of the ovum, 176.

Adaptability, indicative of dominance, 258.

Adaptation, 217; and acquired characters, 219; and changes of morphology and function, 219; not inherited, 220; causes of, 239.

Adaptive response, 219.

Adiabatic changes, 361.

Aggregates, molecular, 353.

Algæ, distribution of, 260.

Allelomorphs, Mendelian, 231.

Alternation of generations, 175.

Amido-substances, 88.

Anabolism, 88.

Anatomical parts, homologies of, 251.

Animal action, considered objectively, 278.

Animal and plant contrasted, 269.

Animality, 269.

Annectant forms of life, 253.

Annelids, morphology of, 248.

Anthropomorphism in theories of action, 148.

Anti-enzymes, 94.

Antitoxins, 36.

Ants, a dominant group, 260.

Appendix vermiformis, 250.

Approximation, standards of, 347.

Armoured animals, 263.

Arthropods, morphology of, 249; a dominant group, 259; distribution, 260; musculature of, 275; adaptations for mobility, 275; limits to size of, 275.

Assimilation, 67.

Atoms, constitution of, 355; arrangements of, 353.

Automatism of animals deduced from mechanistic theories, 280.

Autonomy in development, 322.

Available energy, 62; and entropy, 374.

Bacteria, a dominant group, 259; distribution, 259; geological history, 259, 261; morphology, 268; metabolism, 266; specialisation, 263; parasitism, 259; nitrogen, 73; prototrophic, 119, 266; paratrophic, 266; putrefactive, 266; fermentation, 266; and Brownian movements, 119; compensatory to plants, 267.

Bergson, 28; creative evolution, 244; duration, 154; animals and plants, 78; eye of Pecten, 234; inert matter, 375; infinitesimal analysis of the organism, 111; kinematographic analysis, 110; theory of intellectualism, 51; memory, 156; morphological themes, 250; theory of pain, 281; theory of perception, 7, 10; the vital impetus, 318.

Biology, systematic, 201, 203.

Biophors, 132; size of, 183; growth of, 185.

Biotic energy, 325.

Borelli and animal mechanism, 125.

Brownian movement, 118; significance of, 119.

Bryan and thermodynamics, 62.

Bud-formation, 165.

Calculus, infinitesimal, 25, 115, 350.

Calorimetric experiments, 65, 68.

Capacity-energy factors, 61.

Carnot’s cycle, 69, 78, 113; negative, 368; description of, 363, 366; compared with plant metabolism, 75; compared with the organism, 73.

Catalysis, 90; universality of, 91.

Catalysts, characters of, 91.

Categories of organisms, 209.

Central nervous system, specialisation of, 273; a switchboard, 273; evolution of, parallel with evolution of muscular system, 281.

Chance in evolution, 237.

Chemical affinity, 361.

Chemical energy, degradation of, 75.

Chemical reactions, direction of, 78; exothermic, 86; explosive, 86; similar in organic and inorganic systems, 78.

Chemical synthesis, involve vital activity, 318.

Chemistry, medieval, 125.

Chlorophyll, 69.

Chlorophyllian organisms, 88; metabolism of, 265; a dominant group, 259; essential morphology of, 268; distribution of, 260.

Chromatin of the nucleus, 130; the material basis of inheritance, 182.

Chromosomes, 130, 182, 183.

Classification of organisms, 209.

Classificatory systems, are artificial arrangements, 289; suggest evolutionary process, 210.

Clausius, 54; and Carnot’s Law, 113.

Cœlenterates, morphology of, 248.

Cœlomate animals, 256.

Colloidal platinum, 91.

Colloids, 107.

Colonial organisms, 164.

Comparative anatomy, task of, 251.

Compensatory energy-transformations effected by life, 309.

Conjugation, 173; and heredity, 176; a stimulus to growth, 175.

Consciousness involves analysis of the environment, 11; analysis of, is an arbitrary process, 12; a feeling of normality, 6; a part of crude sensation, 40; simplified by reasoning, 41; an intensive multiplicity, 303; degree of, is parallel to development of sensori-motor system, 280; not existent outside ourselves, 278; not a function of chemico-physical mechanism, 160; intense in difficultly performed operations, 281; and activity of cerebral cortex, 281; absent in parasites, 291.

Conservation a test of reality, 357.

Conservation of energy, 52; in organisms, 83.

Conservation of structure, 253, 256.

Constants, mathematical, 344.

Continuity of cells in embryo, 171.

Contractility, 100; muscular, 103.

Co-ordinates, systems of, 23.

Corals, 164.

Cosmic evolution, 314; is a tendency towards degradation of energy, 316.

Creation, special, 214.

Curvature, 27.

Curves, isothermal and adiabatic, 362.

Cuttle-fishes, 250.

Cytoplasm, 130.

Darwin, and natural selection, 221; acquired characters are inherited, 220; hypothesis of pangenesis, 181.

Death, is catastrophic katabolism, 340.

Degradation of energy, 81.

Deliberation and consciousness, 281.

Demons, Maxwell’s, 116.

Descartes and mechanism, 121; the rational soul, 123, 318; his physiology, 122; his spiritualism, 124; and animal automatism, 125.

Descent, collateral, 257.

Determinants in embryology, 132, 183; arrangement of, 184; latent in regenerative processes, 142.

Development, organisation in, 128; parthenogenetic, 176; reverses inorganic tendencies, 324; impossibility of chemical hypotheses, 141; is the assumption of a mosaic structure, 301; blastula stage in, 129; gastrula stage in, 130; pluteus stage in, 140; individual, 300.

Developmental systems prospective value of, 138; prospective potency of, 138.

Diatoms, 163; distribution of, 260.

Differential elements, 115.

Differentiation in development, 170.

Diffusion in the animal body, 95.

Digestion, 67; chemistry of, 72.

Dinosaurs, an unsuccessful line of evolution, 275.

Dissipation of energy, 114; in physical mechanisms, 59; by the organism, 68, 79.

Distribution of organisms, 262; limits to, 259; indicative of dominance, 258.

Diversity, physical, 54; effective and ineffective, 115.

Dominance in geological time, 258; implies long geological history, 261; Mendelian, 196.

Dominant organisms, 258, 259, 264.

Driesch natural selection, 229; analytical definition of the organism, 331; entelechy, 318; experimental embryology, 134; historical basis of reacting, 154; logical proof of vitalism, 136; proof of vitalism from behaviour, 153; theory of the absolute, 47.

Duration, 28; duration and time illustrated, 30; illustrated by immunity, 35; more than memory, 155; a factor in responding, 155.

Ecdysis, 276.

Echinoderms, morphology of, 248.

Ectoderm, 177.

Effector organs, 158, 271.

Élan vital, 161.

Electromagnetism, 355.

Electrons, 304, 355.

Elimination, natural, 229.

Embryological stages compared with physical phases, 308.

Embryology, 127; hypotheses of, 128; physical hypotheses fail, 128; experimental, 128; suggests phylogenetic history, 213.

Emulsoids, 108.

Endoskeleton, 177, 276.

Energetics, first law of, 51; second law of, 113.

Energy, 356; available and unavailable, 55; biotic, 325; chemical, 61; and causation, 54; degradation of, 63; dissipation of, 53; electrical, 61; forms of, 325; kinetic, 52, 357; mechanical, 60, 61; potential, 53, 358; of position, 360.

Energy-transformations, 54, 371; anabolic, 89; in the animal, 70; compensatory, 88; compensatory organic, 268; irreversible, 59; in physical mechanisms, 58; in the plant, 71.

Engelmann, and the artificial muscle, 105.

Entelechy, 161, 318; not energy, 329; is power of direction, 329; not spatial but acts into space, 330; an intensive manifoldness, 330; is arrangement, 323; involves regulations, 323; arrests inorganic happening, 327; initiates chemical happening, 327; compared with enzyme action, 327; illustrated by analogy, 322.

Entropy, 54; augmentation of, 75; and Carnot engine, 369.

Environment, does not select variations, 235; made by the organism, 236.

Enzymes, 90; nature of, 92; pancreatic, 93; reversible, 93; activation of, 92.

Enzyme activity, 93.

Epigenesis in development, 129.

Equilibrium, chemical, 102. false, 86, 151.

Ether of space, 46, 304, 361; potential energy resides in, 361.

Evolution tendencies of, 252, 264, 276, 295; separation of tendencies, 296; a transformation of intensive into extensive manifoldness, 309; a dissociation of tendencies originally coalescent, 305; increases diversity, 310; segregates energy, 311; compared with permutations and combinations, 301; a series of phases in a transforming system, 298; a logical hypothesis, 214; parallel processes in, 234; geological time inadequate for, 237; side paths in, 262; mechanistic hypotheses inadequate, 237; cosmic, 214, 297, 314; of the crust of the earth, 264.

Excretory products, 269.

Exoskeleton, 276.

Exothermic reactions, 86.

Experience and duration, 156.

Experimental biology proves evolution, 246.

Explosive reactions, 101.

Extension in space, 18.

Extinct groups, 263.

Fats, digestion of, 93.

Fecundity of animals, 179, 239.

Ferments, 92.

Fertilisation (in reproduction), 176.

Finalism, 216.

Fishes, distribution of, 261.

Fluctuating variations, 200.

Food-stuffs, absorption of, 89.

Force, 354.

Form, accidental and essential, 167, 353; geological, 168; crystalline, 168.

Frequency distributions, 22, 187, 350.

Frog, development of egg of, 131.

Functionality, 343; in physical systems, 307.

Galvanotropism, 145.

Gases, compression of, 362; kinetic theory of, 117, 361.

Gastrea-theory, 177; illustrated, 255; limitations of, 256.

Genera, stability of, 186.

Geometry, Cartesian, 25; Euclidean, 19, 25; perceptual and conceptual limits, 21.

Geotropism, 144.

Germ-cells, 175; and soma, 179.

Germinal selection, 241.

Germ-layers, 177; theory of, 256.

Germ-plasm, a mixture, 240; stability of, 240.

Givenness, 47.

Gonads, 179.

Growth law of, in the organism, 172; by accretion, 169; by ecdysis, 276; geometrical, 169; physical, 167; of crystals, 167; and differentiation, 170; variability of, 172.

Haeckel, the Gastrea-Theorie, 177, 254.

Harmonic analysis, 11.

Harvey, and the circulation of the blood, 121.

Heat, flow of, 117; production of, in physical changes, 114.

Heliotropism, 144.

Heredity, 181.

Hertzian waves, 355.

Homoiothermic animals, 67.

Hormones, 225.

Human activity, tends to arrest dissipation of energy, 312.

Huxley, 84; and mechanistic biology, 127; and the physical basis of life, 113; and mechanism, 106; and universal mathematics, 215.

Hybrids, Mendelian, 196; infertility of, 195; between Linnean species, 194.

Hydra, regeneration of, 162.

Idants, 183.

Idealism founded on pure reasoning, 45; of Berkeley, 45.

Ids, 183.

Immunity, 35.

Individual, 162; definition of, 167.

Individuality, orders of, 163; physical concept of, 165; morphologically an artificial concept, 166; in societies, 171.

Inertia, 354.

Infinity, a definition of, 342.

Inorganic happening abolishes diversity, 310.

Instinct, a problem for naturalists, 283; an inheritable adaptation of behaviour, 287.

Instinct and intelligence, 283; distinction not absolute, 294; may coexist, 306.

Instinct and functioning, 286.

Instinctive actions not necessarily unconscious, 283; not learned, 286; not necessarily perfect, 284; effective from the first, 285; capable of improvement, 285.

Intelligent actions, non-inheritable adaptations of behaviour, 287; involve deliberation, 50, 287; involve conscious relations with the environment, 288; involve use of tools, 284.

Intensity-factors, 61.

Intensive multiplicity, 303.

Irreversibility, 62.

Irritability, 100.

Isothermal changes, 361.

James, William (and academic philosophies), 80.

Jennings, and physiological states, 154; behaviour of Protozoa, 293; animal movements, 149; the avoiding reaction, 149.

Katabolism, 90.

Kinases, 92.

Kinematographic analysis, 316.

Lamarck, hypotheses of evolution, 220.

Lamarckian inheritance, an inadequate cause of transformism, 227.

Lankester, acquired characters not inherited, 221.

Laplace, and universal mathematics, 215.

Laplacian mind, 299.

Larval stages, 170.

Latency (of characters), 195.

Lavoisier, and chemistry of the organism, 127.

Life and adaptation to physical conditions, 338; and reversibility, 339; a direction of energies, 341; defined energetically, 337; cosmic origin of, 338; physical conditions for, 338; limited in power, 306; sparsity of, on the earth, 306; tends to arrest dissipation of energy, 314; its origin a pseudo-problem, 337.

Life-substance, the primitive, 301.

Locomotion, 258.

Loeb and the associative memory, 155; and artificial parthenogenesis, 176; mechanism and life, 127; stereotropism, 19; theory of tropisms, 144; tropistic movements, 146; theories of heredity, 181.

Limit, the mathematical, 346.

Limits to perceptual activity, 23.

Links, missing, 252.

Linnean species, 201.

Manifoldness, intensive, 302.

Mass, 353.

Mass action, 140.

Materialism, 85.

Mathematics, evades consideration of time, 35.

Matter, 353; inert, 375; notion of is an intuitive one, 352.

Maxwell, and sorting demons, 116, 377.

Mayow, and chemical physiology, 126.

Mechanical work, done by the animal, 67; not done by the plant, 71.

Mechanism, organic and inorganic, 78; the thermodynamic, 66; radical, 215; in life, 121.

Membranes, semi-permeable, 95.

Memory, 39; a possible cerebral mechanism of, 158; mechanistic hypotheses impossible, 157.

Mendelism, 196; a logical hypothesis, 199; terminology is a symbolism, 198; analogy of unit characters with chemical radicles, 197; transmission of characters of, 230.

Mesoderm, 177; origin of, 255.

Metabolism, 37, 88, 209; analytic, 269; of animals, 65, 67; constructive, 269; destructive, 269; direction of, 69; in green plant, 70, 75; intra-cellular, 99; integration of its activities, 111; rôle of oxygen in, 105; specialisation of during evolution, 305; synthetic, 269.

Metaphysics of science, 45.

Metazoan animals, 162.

Mitosis, 182.

Mobility, organic, 269; structural adaptations tending to, 275.

Modifications of structure adaptive and non-adaptive, 251.

Molecules, 353; size of, 116; in a gas, 115; aggregations of, 108.

Molluscs, morphology of, 249.

Morgan, and physico-chemical mechanisms, 128, 143.

Morphogenesis, 257.

Morphological evolution, tendencies of, 295.

Morphological structures degeneration of, 251; suppression of, 250; coalescence of, 250; replacement of, 250; specialisation of, 250; change of function of, 251.

Morphology, 209; a basis of classification, 210; relates groups of organisms, 211; distinctions of, not absolute, 285, 290; generalised, 250; suggests blood relationships, 213; schemata of, 249, 291; cannot be considered apart from physiology, 285.

Mosaic-theory of development, 131.

Motion not an intellectual concept, 27; not considered in Euclidean or Cartesian geometry, 26; bodily motion is absolute, 24; outside ourselves is relative, 24.

Motor-habits, 38, 155.

Multicellular organisms, evolution of, 223.

Muscular contraction, 104; metabolism in, 104; heat production in, 104.

Muscular and nervous organs, 275.

Musculature and weight of body, 275.

Mutations, 189; essential nature of, 193; causes of, 200; must be co-ordinated, 231; physical model of, 192; the material for selection, 230.

Nägeli, and autonomy in development, 160.

Natural selection, 228; generality of, 229; a slow process, 230.

Nebulæ, 315.

Nebular hypothesis, 296.

Nerve impulses, 100; velocity of, 101; integration of, 273.

Nervous system, 272; in co-ordination of activities, 171; paths in, 157.

Nervous activity, 107; metabolism in, 107; electric changes in, 107; influence of metabolism on, 97.

Nothing, a pseudo-idea, 18.

Nucleus, evolution of, 222; division of, 130, 182.

Ontogenetic stages, 255.

Orders of individuality, 171.

Organism, definition of, 331; analysis of its activities, 109; animal and plant, 76; considered energetically, 77; the dominant, 258; a function of the environment, 216; a mechanism, 51; the primitive, 222; a physico-chemical system, 65; a thermodynamic mechanism, 104.

Organic chemical syntheses, 317.

Organisation in development, 137.

Organ-rudiments, 257.

Osmosis, 95, 99.

Ostracoderms, 291.

Ostwald on catalysis, 91.

Ovum, development of, 129; maturation of, 198, 239; an intensive manifoldness, 302.

Oxidases, 105.

Oxygen in metabolism, 69.

Pain, Bergson on, 281.

Palæontology, 210; relates groups of organisms, 211.

Pangenesis, 181.

Paramœcium, division of, 173, 175; responses of, 4.

Parasitism, 259; tends to immobility, 290.

Parthenogenesis, 176; artificial, 176.

Particles, 356.

Pecten, eye of, 233.

Perception not merely physical stimulation, 7; involves effector activity, 7; involves deliberative action, 9; arises from acting, 50; and choice of response, 155; is unfamiliar cerebral activity, 8; skeletonises consciousness, 40.

Peridinians, 77, 163; distribution of, 260.

Personal equation, 45.

Personality, 167; an intuition, 167; division of, 173; is absolute, 48.

Pflüger, and experimental embryology, 131.

Phases in physical systems and organic systems, 321; in transforming systems, 308.

Phenomenalism, 46.

Photosynthesis, 70, 76, 86.

Phototaxis, 144.

Phyla animal, 247; morphology of, 247; relations between, 252; ancestries of, 252.

Phylogenies, 253; are summaries of morphological results, 254; indicative of directions of evolution, 254; criteria of, 253.

Phylogeny, 246.

Phylum, 210.

Physical basis of life, 84.

Physico-chemical reactions, 80; are directed, 118; the means of development and behaviour in the organism, 160.

Physico-psychical parallelism, 160.

Physics, a statistical science, 116, 377.

Physiology Galenic, 122; an analysis of organic activity, 120, 328.

Plants, geological history of, 261; characterised by immobility, 277; contrasted with animals, 277.

Platonic ideas, 204.

Platyhelminths, morphology of, 248.

Poikilothermic animals, 68.

Poincaré, and Brownian movement, 119.

Polar bodies, 198.

Polyzoa, 164.

Porifera, 248.

Potential, 61.

Potential energy, 58, 114.

Preformation an embryological hypothesis, 128.

Probability, 350.

Proteids, digestion of, 90.

Proto-forms, 254.

Protoplasm, nature of, 106; artificial, 106; disintegration of, 107; activities of, 107; similar in plant and animal, 294.

Protozoa, 247; behaviour of, 293.

Pterodactyls, 274.

Races (in specific groups), 194.

Radiation, 355; of sun, 51; transformation of energy of, 57.

Radio-activity, 56, 359.

Reality, objective, 43.

Reception, 3; organs of, 271; by specialised sense-organs, 11.

Recessiveness, Mendelian, 196.

Reflex action, 4, 272; concatenated, 150; a complex series of actions, 6; not necessarily accompanied by perception, 155; the basis of instincts, 150; a schematic description, 5; in decapitated frog, 6; frictionless cerebral activity, 8; involves a limited part of the environment, 50.

Reflex arcs, 272.

Regeneration, 142; in Hydra, 164; in sea-urchin embryo, 164; in Planaria, 164.

Regression, 189.

Reinke, and structure of protoplasm, 106.

Reintegration in development, 171.

Rejuvenescence, 175.

Releasing agencies, 157.

Reproduction, 167; asexual, 175; by brood-formation, 173; by conjugation, 173; sexual, 174; by division, 172; compared with minting machine, 242; of the tissues, 180.

Responses of organisms, 217; directed, 269; of magnet, 279; of green plant, 279.

Reversibility, physical, 369.

Rodewald, chemical nature of protoplasm, 106.

Roux, experimental embryology, 131; development the production of a visible manifoldness, 307.

Saliva, secretion of, 96.

Salivary glands, metabolism of, 96.

Salivary secretion, not a purely mechanistic process, 112.

Sea, not really rich in life, 306.

Sea-urchin gastrula, 170.

Secretion described mechanistically, 98.

Secretion, psychical, 99.

Segmentation of the ovum, 129.

Selection, natural, 228; from fluctuating variations, 189; from mutations, 190.

Semon, mnemic hypothesis of heredity, 181.

Senescence, 175.

Sensation, 2; analysis of, 13.

Sense-receptors and the idea of matter, 352.

Sensori-motor system, 270; dominant in animals, 271, 273; specialisation of, 271, 273; essentially the same in all animals, 294; absent in plants, 269; vestigial in some parasites, 290.

Sexuality, 174.

Siphonophores, regeneration in, 163.

Size of animals, 274.

Skeleton of vertebrates, 276; of arthropods, 276; and mobility, 276.

Soddy, and chemical energy, 361.

Soma, 179; evolution of, 223.

Space, form of, 18; 3-dimensional, 18; 3-dimensional space an intuition, 19; 2-dimensional, 19; the form of, depends on modes of activity, 21, 25.

Species, are categories of structure, 201; comparison with Platonic ideas, 204; criteria of, 202; elementary, 193; are intellectual constructions, 203; individuality of, 203; Linnean, 201, 289; are phases in an evolutionary flux, 206; are families in the human sense, 208; systematic, 201.

Specific organisation, stability of, 186.

Stahl, and the phlogistic hypothesis, 126; and vitalism, 126.

Stimuli, elemental, 151; physico-chemical, 151; formative, 176; complex auditory, 152; integration of, 152; individualised, 152, 270; contractile, 103.

Stimulus and response, functionality of, 152.

Substantia physica, 46, 355.

Surface tension, 105, 106.

Suspensoids, 108.

Sylvius, the organism a chemical mechanism, 125.

Symbiosis, 77.

Symbiotic organisms, 88.

Synapses, in central nervous system, 158, 272.

Synthetic chemistry, 236, 317.

System, isolated, 63.

Systems in development equipotential, 139; harmonious equipotential, 139; complex equipotential, 140.

Taxis, 144; no perception in, 155.

Telegraphy, wireless, 355.

Temperature of sun, 56; of space, 57.

Thermodynamics, 51; 1st law of, 51; 2nd law of, 54, 63, 309, 316; and Maxwell’s demons, 118; laws of subject to limitations, 115.

Thermodynamical mechanism, the organism not a, 69.

Thomson, W., dissipation of energy, 113.

Time a series of standard events, 28; astronomical, 34; time differentials, 34.

Tissues, evolution of, 223.

Tools, nature of, 285; use of must be learned, 285; bodily, 285.

Toxins, 36.

Transformism, 213.

Trematodes, larval stages of, 165.

Trial and error, 293; in reasoning, 293; a hypothesis of animal movements, 150.

Trigger reactions, 87.

Trilobites, an ancient group, 261.

Tropisms, 144; in plants, 269, 279; in moths, 280; and natural selection, 147; and movements of caterpillars, 146; an inadequate basis for a theory of animal movements, 147.

Tunicates, suppressed notochord of, 250.

Unavailable energy and entropy, 375; tendency to increase of, 375.

Unicellular organisms, energy-transformations in, 177.

Unit-characters, 230.

Van’t Hoff’s law, 218.

Variability, 172, 186; continuous, 188; discontinuous, 188; examples of, 187; and the environment, 189; independent of the environment, 239; and growth, 188; tendencies of, 235.

Variation, rate of (mathematical), 344; in biology, 186; atavistic, 195; direction of, 233; fluctuating, 189; must be co-ordinated, 231; mathematical probability of co-ordination of 233; the material for selection, 229; origin of, 230; selected by the organism, 237; cause of, a pseudo-problem, 242; arise de novo, 244.

Variables (mathematical), 343.

Varieties, specific, 194.

Vegetable life, 265.

Vertebrates, 249; adaptations securing mobility, 275; ancestry of, 253; morphology of, 249; a dominant group, 259; distribution of, 260.

Verworn, and mechanism in life, 127.

Vesalius, anatomical school of, 121.

Vital activities, integration of, 128; co-ordination of, 171.

de Vries and mutations, 191; fluctuating variations inherited, 220.

Vital force, 318.

Van der Waal’s equation, 308.

Weber’s law, 16; a quasi-mathematical relation, 17.

Weismann, hypothesis of heredity, 182; hypothesis of germinal selection, 241; hypothesis of development, 132; mosaic-theory, 131; preformation hypothesis, 133; hypothesis of the germ-plasm, continuity of the germ-plasm, 181; germinal changes inconceivable, 224; size of biophors, 183; origin of life, 339; spontaneous generation a logical necessity, 339.

Weismannism, a series of logical hypotheses, 320; physico-chemical analogies, and subsidiary hypotheses, 223.

Whales, an unsuccessful line of evolution, 274.

Whitehead, and mathematical reasoning, 347.

Wilson, mosaic-theory of development, 139.

Yerkes, and behaviour of crustacea, 293.

Zymogens, 92.

Zymoids, 94.

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Spelling corrections:

animo-acids → amino-acids animo-substances → amino-substances differen tkinds → different kinds algae → algæ organsim → organism (x2) diffusbility → diffusibility marjoity → majority hythothesis → hypothesis execretory → excretory conconsidered → considered