CHAPTER VIII

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.[32] 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.

[32] 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.[33] 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?

[33] 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.[34]

[34] 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[35]

[35] 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.

[Illustration: FIG. 27.]

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_.

[Illustration: FIG. 28.]

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.[36]

[36] 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

δ_s_/δ_t_, where δ_s_ is a very small interval of path containing

the point chosen, but not as an end-point, and δ_t_ 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 δ_s_

is still a finite interval, and δ_t_ 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 δ_s_, the closer will be this

approximation. Suppose, then, that we diminish δ_s_ till it “becomes

zero.” It might appear now that when δ_s_ 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 δ_s_/δ_t_ 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.