The Principles of Biology Vol. I/Chapter II.1

by Herbert Spencer

PART II.

THE INDUCTIONS OF BIOLOGY.

CHAPTER I.

GROWTH.

§ 43. Perhaps the widest and most familiar induction of Biology, is that organisms grow. While, however, this is a characteristic so uniformly and markedly displayed by plants and animals, as to be carelessly thought peculiar to them, it is really not so. Under appropriate conditions, increase of size takes place in inorganic aggregates, as well as in organic aggregates. Crystals grow; and often far more rapidly than living bodies. Where the requisite materials are supplied in the requisite forms, growth may be witnessed in non-crystalline masses: instance the fungous-like accumulation of carbon that takes place on the wick of an unsnuffed candle. On an immensely larger scale, we have growth in geologic formations: the slow accumulation of deposited sediment into a stratum, is not distinguishable from growth in its widest acceptation. And if we go back to the genesis of celestial bodies, assuming them to have arisen by Evolution, these, too, must have gradually passed into their concrete shapes through processes of growth. Growth is, indeed, as being an integration of matter, the primary trait of Evolution; and if Evolution of one kind or other is universal, growth is universal—universal, that is, in the sense that all aggregates display it in some way at some period.

The essential community of nature between organic growth and inorganic growth, is, however, most clearly seen on observing that they both result in the same way. The segregation of different kinds of detritus from each other, as well as from the water carrying them, and their aggregation into distinct strata, is but an instance of a universal tendency towards the union of like units and the parting of unlike units (First Principles, § 163). The deposit of a crystal from a solution is a differentiation of the previously mixed molecules; and an integration of one class of molecules into a solid body, and the other class into a liquid solvent. Is not the growth of an organism an essentially similar process? Around a plant there exist certain elements like the elements which form its substance; and its increase of size is effected by continually integrating these surrounding like elements with itself. Nor does the animal fundamentally differ in this respect from the plant or the crystal. Its food is a portion of the environing matter that contains some compound atoms like some of the compound atoms constituting its tissues; and either through simple imbibition or through digestion, the animal eventually integrates with itself, units like those of which it is built up, and leaves behind the unlike units. To prevent misconception, it may be well to point out that growth, as here defined, must be distinguished from certain apparent and real augmentations of bulk which simulate it. Thus, the long, white potato-shoots thrown out in the dark, are produced at the expense of the substances which the tuber contains: they illustrate not the accumulation of organic matter, but simply its re-composition and re-arrangement. Certain animal-embryos, again, during their early stages, increase considerably in size without assimilating any solids from the environment; and they do this by absorbing the surrounding water. Even in the highest organisms, as in children, there appears sometimes to occur a rapid gain in dimensions which does not truly measure the added quantity of organic matter; but is in part due to changes analogous to those just named. Alterations of this kind must not be confounded with that growth, properly so called, of which we have here to treat.

The next general fact to be noted respecting organic growth, is, that it has limits. Here there appears to be a distinction between organic and inorganic growth; but this distinction is by no means definite. Though that aggregation of inanimate matter which simple attraction produces, may go on without end; yet there appears to be an end to that more definite kind of aggregation which results from polar attraction. Different elements and compounds habitually form crystals more or less unlike in their sizes; and each seems to have a size that is not usually exceeded without a tendency arising to form new crystals rather than to increase the old. On looking at the organic kingdom as a whole, we see that the limits between which growth ranges are very wide apart. At the one extreme we have monads so minute as to be rendered but imperfectly visible by microscopes of the highest power; and at the other extreme we have trees of 400 to 500 feet high and animals of 100 feet long. It is true that though in one sense this contrast may be legitimately drawn, yet in another sense it may not; since these largest organisms arise by the combination of units which are individually like the smallest. A single plant of the genus Protococcus, is of the same essential structure as one of the many cells united to form the thallus of some higher Alga, or the leaf of a phænogam. Each separate shoot of a phænogam is usually the bearer of many leaves. And a tree is an assemblage of numerous united shoots. One of these great teleophytes is thus an aggregate of aggregates of aggregates of units, which severally resemble protophytes in their sizes and structures; and a like building up is traceable throughout a considerable part of the animal kingdom. Even, however, when we bear in mind this qualification, and make our comparisons between organisms of the same degree of composition, we still find the limit of growth to have a great range. The smallest branched flowering plant is extremely insignificant by the side of a forest tree; and there is an enormous difference in bulk between the least and the greatest mammal. But on comparing members of the same species, we discover the limit of growth to be much less variable. Among the Protozoa and Protophyta, each kind has a tolerably constant adult size; and among the most complex organisms the differences between those of the same kind which have reached maturity, are usually not very great. The compound plants do, indeed, sometimes present marked contrasts between stunted and well-grown individuals; but the higher animals diverge but inconsiderably from the average standards of their species.

On surveying the facts with a view of empirically generalizing the causes of these differences, we are soon made aware that by variously combining and conflicting with one another, these causes produce great irregularities of result. It becomes manifest that no one of them can be traced to its consequences, unqualified by the rest. Hence the several statements contained in the following paragraphs must be taken as subject to mutual modification.

Let us consider first the connexion between degree of growth and complexity of structure. This connexion, being involved with many others, becomes apparent only on so averaging the comparisons as to eliminate differences among the rest. Nor does it hold at all where the conditions are radically dissimilar, as between plants and animals. But bearing in mind these qualifications, we shall see that organization has a determining influence on increase of mass. Of plants the lowest, classed as Thallophytes, usually attain no considerable size. Algæ, Fungi, and the Lichens formed by association of them count among their numbers but few bulky species: the largest, such as certain Algæ found in antarctic seas, not serving greatly to raise the average; and these gigantic seaweeds possess a considerable complexity of histological organization very markedly exceeding that of their smaller allies. Though among Bryophytes and Pteridophytes there are some, as the Tree-ferns, which attain a considerable height, the majority are but of humble growth. The Monocotyledons, including at one extreme small grasses and at the other tall palms, show us an average and a maximum greater than that reached by the Pteridophytes. And the Monocotyledons are exceeded by the Dicotyledons; among which are found the monarchs of the vegetal kingdom. Passing to animals, we meet the fact that the size attained by Vertebrata is usually much greater than the size attained by Invertebrata. Of invertebrate animals the smallest, classed as Protozoa, are also the simplest; and the largest, belonging to the Annulosa and Mollusca, are among the most complex of their respective types. Of vertebrate animals we see that the greatest are Mammals, and that though, in past epochs, there were Reptiles of vast bulks, their bulks did not equal that of the whale: the great Dinosaurs, though as long, being nothing like as massive. Between reptiles and birds, and between land-vertebrates and water-vertebrates, the relation does not hold: the conditions of existence being in these cases widely different. But among fishes as a class, and among reptiles as a class, it is observable that, speaking generally, the larger species are framed on the higher types. The critical reader, who has mentally checked these statements in passing them, has doubtless already seen that this relation is not a dependence of organization on growth but a dependence of growth on organization. The majority of Dicotyledons are smaller than some Monocotyledons; many Monocotyledons are exceeded in size by certain Pteridophytes; and even among Thallophytes, the least developed among compound plants, there are kinds of a size which many plants of the highest order do not reach. Similarly among animals. There are plenty of Crustaceans less than Actiniæ; numerous reptiles are smaller than some fish; the majority of mammals are inferior in bulk to the largest reptiles; and in the contrast between a mouse and a well-grown Medusa, we see a creature that is elevated in type of structure exceeded in mass by one that is extremely low. Clearly then, it cannot be held that high organization is habitually accompanied by great size. The proposition here illustrated is the converse one, that great size is habitually accompanied by high organization. The conspicuous facts that the largest species of both animals and vegetals belong to the highest classes, and that throughout their various sub-classes the higher usually contain the more bulky forms, show this connexion as clearly as we can expect it to be shown, amid so many modifying causes and conditions.

The relation between growth and supply of available nutriment, is too familiar a relation to need proving. There are, however, some aspects of it that must be contemplated before its implications can be fully appreciated. Among plants, which are all constantly in contact with the gaseous, liquid, and solid matters to be incorporated with their tissues, and which, in the same locality, receive not very unlike amounts of light and heat, differences in the supplies of available nutriment have but a subordinate connexion with differences of growth. Though in a cluster of herbs springing up from the seeds let fall by a parent, the greater sizes of some than of others is doubtless due to better nutrition, consequent on accidental advantages; yet no such interpretation can be given of the contrast in size between these herbs and an adjacent tree. Other conditions here come into play: one of the most important being, an absence in the one case, and presence in the other, of an ability to secrete such a quantity of ligneous fibre as will produce a stem capable of supporting a large growth. Among animals, however, which (excepting some Entozoa) differ from plants in this, that instead of bathing their surfaces the matters they subsist on are dispersed, and have to be obtained, the relation between available food and growth is shown with more regularity. The Protozoa, living on microscopic fragments of organic matter contained in the surrounding water, are unable, during their brief lives, to accumulate any considerable quantity of nutriment. Polyzoa, having for food these scarcely visible members of the animal kingdom, are, though large compared with their prey, small as measured by other standards; even when aggregated into groups of many individuals, which severally catch food for the common weal, they are often so inconspicuous as readily to be passed over by the unobservant. And if from this point upwards we survey the successive grades of animals, it becomes manifest that, in proportion as the size is great, the masses of nutriment are either large, or, what is practically the same thing, are so abundant and so grouped that large quantities may be readily taken in. Though, for example, the greatest of mammals, the arctic whale, feeds on such comparatively small creatures as the acalephes and molluscs floating in the seas it inhabits, its method of gulping in whole shoals of them and filtering away the accompanying water, enables it to secure great quantities of food. We may then with safety say that, other things equal, the growth of an animal depends on the abundance and sizes of the masses of nutriment which its powers enable it to appropriate. Perhaps it may be needful to add that, in interpreting this statement, the proportion of competitors must be taken into account. Clearly, not the absolute, but the relative, abundance of fit food is the point; and this relative abundance very much depends on the number of individuals competing for the food. Thus all who have had experience in fishing in Highland lochs, know that where the trout are numerous they are small, and that where they are comparatively large they are comparatively few.

What is the relation between growth and expenditure of energy? is a question which next presents itself. Though there is reason to believe such a relation exists, it is not very readily traced: involved as it is with so many other relations. Some contrasts, however, may be pointed out that appear to give evidence of it. Passing over the vegetal kingdom, throughout which the expenditure of force is too small to allow of such a relation being visible, let us seek in the animal kingdom, some case where classes otherwise allied, are contrasted in their locomotive activities. Let us compare birds on the one hand, with reptiles and mammals on the other. It is an accepted doctrine that birds are organized on a type closely allied to the reptilian type, but superior to it; and though in some respects the organization of birds is inferior to that of mammals, yet in other respects, as in the greater heterogeneity and integration of the skeleton, the more complex development of the respiratory system, and the higher temperature of the blood, it may be held that birds stand above mammals. Hence were growth dependent only on organization, we might infer that the limit of growth among birds should not be much short of that among mammals; and that the bird-type should admit of a larger growth than the reptile-type. Again, we see no manifest disadvantages under which birds labour in obtaining food, but from which reptiles and mammals are free. On the contrary, birds are able to get at food that is fixed beyond the reach of reptiles and mammals; and can catch food that is too swift of movement to be ordinarily caught by reptiles and mammals. Nevertheless, the limit of growth in birds falls far below that reached by reptiles and mammals. With what other contrast between these classes, is this contrast connected? May we not suspect that it is connected (partially though not wholly) with the contrast between their amounts of locomotive exertion? Whereas mammals (excepting bats, which are small), are during all their movements supported by solid surfaces or dense liquids; and whereas reptiles (excepting the ancient pterodactyles, which were not very large), are similarly restricted in their spheres of movement; the majority of birds move more or less habitually through a rare medium, in which they cannot support themselves without relatively great efforts. And this general fact may be joined with the special fact, that those members of the class Aves, as the Dinornis and Epiornis, which approached in size to the larger Mammalia and Reptilia, were creatures incapable of flight—creatures which did not expend this excess of force in locomotion. But as implied above, and as will presently be shown, another factor of importance comes into play; so that perhaps the safest evidence that there is an antagonism between the increase of bulk and the quantity of motion evolved is that supplied by the general experience, that human beings and domestic animals, when overworked while growing, are prevented from attaining the ordinary dimensions.

One other general truth concerning degrees of growth, must be set down. It is a rule, having exceptions of no great importance, that large organisms commence their separate existences as masses of organic matter more or less considerable in size, and commonly with organizations more or less advanced; and that throughout each organic sub-kingdom, there is a certain general, though irregular, relation between the initial and the final bulks. Vegetals exhibit this relation less manifestly than animals. Yet though, among the plants that begin life as minute spores, there are some which, by the aid of an intermediate form, grow to large sizes, the immense majority of them remain small. While, conversely, the great Monocotyledons and Dicotyledons, when thrown off from their parents, have already the formed organs of young plants, to which are attached stores of highly nutritive matter. That is to say, where the young plant consists merely of a centre of development, the ultimate growth is commonly insignificant; but where the growth is to become great, there exists to start with, a developed embryo and a stock of assimilable matter. Throughout the animal kingdom this relation is tolerably manifest though by no means uniform. Save among classes that escape the ordinary requirements of animal life, small germs or eggs do not in most cases give rise to bulky creatures. Where great bulk is to be reached, the young proceeds from an egg of considerable bulk, or is born of considerable bulk ready-organized and partially active. In the class Fishes, or in such of them as are subject to similar conditions of life, some proportion usually obtains between the sizes of the ova and the sizes of the adult individuals; though in the cases of the sturgeon and the tunny there are exceptions, probably determined by the circumstances of oviposition and those of juvenile life. Reptiles have eggs that are smaller in number, and relatively greater in mass, than those of fishes; and throughout this class, too, there is a general congruity between the bulk of the egg and the bulk of the adult creature. As a group, birds show us further limitations in the numbers of their eggs as well as farther increase in their relative sizes; and from the minute eggs of the humming-bird up to the immense ones of the Epiornis, holding several quarts, we see that, speaking generally, the greater the eggs the greater the birds., Finally, among mammals (omitting the marsupials) the young are born, not only of comparatively large sizes, but with advanced organizations; and throughout this sub-division of the Vertebrata, as throughout the others, there is a manifest connexion between the sizes at birth and the sizes at maturity. As having a kindred meaning, there must finally be noted the fact that the young of these highest animals, besides starting in life with bodies of considerable sizes, almost fully organized, are, during subsequent periods of greater or less length, supplied with nutriment—in birds by feeding and in mammals by suckling and afterwards by feeding. So that beyond the mass and organization directly bequeathed, a bird or mammal obtains a further large mass at but little cost to itself.

Were exhaustive treatment of the topic intended, it would be needful to give a paragraph to each of the incidental circumstances by which growth may be aided or restricted:—such facts as that an entozoon is limited by the size of the creature, or even the organ, in which it thrives; that an epizoon, though getting abundant nutriment without appreciable exertion, is restricted to that small bulk at which it escapes ready detection by the animal it infests; that sometimes, as in the weazel, smallness is a condition to successful pursuit of the animals preyed upon; and that in some cases, the advantage of resembling certain other creatures, and so deceiving enemies or prey, becomes an indirect cause of restricted size. But the present purpose is simply to set down those most general relations between growth and other organic traits, which induction leads us to. Having done this, let us go on to inquire whether these general relations can be deductively established.

§ 44. That there must exist a certain dependence of growth on organization, may be shown a priori. When we consider the phenomena of Life, either by themselves or in their relations to surrounding phenomena, we see that, other things equal, the larger the aggregate the greater is the needful complexity of structure.

In plants, even of the highest type, there is a comparatively small mutual dependence of parts: a gathered flower-bud will unfold and flourish for days if its stem be immersed in water; and a shoot cut off from its parent-tree and stuck in the ground will grow. The respective parts having vital activities that are not widely unlike, it is possible for great bulk to be reached without that structural complexity required for combining the actions of parts. Even here, however, we see that for the attainment of great bulk there requires such a degree of organization as shall co-ordinate the functions of roots and branches—we see that such a size as is reached by trees, is not possible without a vascular system enabling the remote organs to utilize each other's products. And we see that such a co-existence of large growth with comparatively low organization as occurs in some of the marine Algæ, occurs where the conditions of existence do not necessitate any considerable mutual dependence of parts—where the near approach of the plant to its medium in specific gravity precludes the need of a well-developed stem, and where all the materials of growth being derived from the water by each portion of the thallus, there requires no apparatus for transferring the crude food materials from part to part. Among animals which, with but few exceptions, are, by the conditions of their existence, required to absorb nutriment through one specialized part of the body, it is clear that there must be a means whereby other parts of the body, to be supported by this nutriment, must have it conveyed to them. It is clear that for an equally efficient maintenance of their nutrition, the parts of a large mass must have a more elaborate propelling and conducting apparatus; and that in proportion as these parts undergo greater waste, a yet higher development of the vascular system is necessitated. Similarly with the prerequisites to those mechanical motions which animals are required to perform. The parts of a mass cannot be made to move, and have their movements so co-ordinated as to produce locomotive and other actions, without certain structural arrangements; and, other things equal, a given amount of such activity requires more involved structural arrangements in a large mass than in a small one. There must at least be a co-ordinating apparatus presenting greater contrasts in its central and peripheral parts.

The qualified dependence of growth on organization, is equally implied when we study it in connexion with that adjustment of inner to outer relations which constitutes Life as phenomenally known to us. In plants this is less striking than in animals, because the adjustment of inner to outer relations does not involve conspicuous motions. Still, it is visible in the fact that the condition on which alone a plant can grow to a great size, is, that it shall, by the development of a massive trunk, present inner relations of forces fitted to counterbalance those outer relations of forces which tend continually, and others which tend occasionally, to overthrow it; and this formation of a core of regularly-arranged woody fibres is an advance in organization. Throughout the animal kingdom this connexion of phenomena is manifest. To obtain materials for growth; to avoid injuries which interfere with growth; and to escape those enemies which bring growth to a sudden end; implies in the organism the means of fitting its movements to meet numerous external co-existences and sequences—implies such various structural arrangements as shall make possible these variously-adapted actions. It cannot be questioned that, everything else remaining constant, a more complex animal, capable of adjusting its conduct to a greater number of surrounding contingencies, will be the better able to secure food and evade damage, and so to increase bulk. And evidently, without any qualification, we may say that a large animal, living under such complex conditions of existence as everywhere obtain, is not possible without comparatively high organization.

While, then, this relation is traversed and obscured by sundry other relations, it cannot but exist. Deductively we see that it must be modified, as inductively we saw that it is modified, by the circumstances amid which each kind of organism is placed, but that it is always a factor in determining the result.

§ 45. That growth is, cæteris paribus, dependent on the supply of assimilable matter, is a proposition so continually illustrated by special experience, as well as so obvious from general experience, that it would scarcely need stating, were it not requisite to notice the qualifications with which it must be taken.

The materials which each organism requires for building itself up, are not of one kind but of several kinds. As a vehicle for transferring matter through their structures, all organisms require water as well as solid constituents; and however abundant the solid constituents there can be no growth in the absence of water. Among the solids supplied, there must be a proportion ranging within certain limits. A plant round which carbonic acid, water, and ammonia exist in the right quantities, may yet be arrested in its growth by a deficiency of potassium. The total absence of lime from its food may stop the formation of a mammal's skeleton: thus dwarfing, if not eventually destroying, the mammal; and this no matter what quantities of other needful colloids and crystalloids are furnished.

Again, the truth that, other things equal, growth varies according to the supply of nutriment, has to be qualified by the condition that the supply shall not exceed the ability to appropriate it. In the vegetal kingdom, the assimilating surface being external and admitting of rapid expansion by the formation of new roots, shoots, and leaves, the effect of this limitation is not conspicuous. By artificially supplying plants with those materials which they have usually the most difficulty in obtaining, we can greatly facilitate their growth; and so can produce striking differences of size in the same species. Even here, however, the effect is confined within the limits of the ability to appropriate; since in the absence of that solar light and heat by the help of which the chief appropriation is carried on, the additional materials for growth are useless. In the animal kingdom this restriction is rigorous. The absorbent surface being, in the great majority of cases, internal; having a comparatively small area, which cannot be greatly enlarged without reconstruction of the whole body; and being in connexion with a vascular system which also must be re-constructed before any considerable increase of nutriment can be made available; it is clear that beyond a certain point, very soon reached, increase of nutriment will not cause increase of growth. On the contrary, if the quantity of food taken in is greatly beyond the digestive and absorbent power, the excess, becoming an obstacle to the regular working of the organism, may retard growth rather than advance it.

While then it is certain, a priori, that there cannot be growth in the absence of such substances as those of which an organism consists; and while it is equally certain that the amount of growth must primarily be governed by the supply of these substances; it is not less certain that extra supply will not produce extra growth, beyond a point very soon reached. Deduction shows to be necessary, as induction makes familiar, the truths that the value of food for purposes of growth depends not on the quantity of the various organizable materials it contains, but on the quantity of the material most needed; that given a right proportion of materials, the pre-existing structure of the organism limits their availability; and that the higher the structure, the sooner is this limit reached.

§ 46. But why should the growth of every organism be finally arrested? Though the rate of increase may, in each case, be necessarily restricted within a narrow range of variation—though the increment that is possible in a given time, cannot exceed a certain amount; yet why should the increments decrease and finally become insensible? Why should not all organisms, when supplied with sufficient materials, continue to grow as long as they live? To find an answer to this question we must revert to the nature and functions of organic matter.

In the first three chapters of Part I, it was shown that plants and animals mainly consist of substances in states of unstable equilibrium—substances which have been raised to this unstable equilibrium by the expenditure of the forces we know as solar radiations, and which give out these forces in other forms on falling into states of stable equilibrium. Leaving out the water, which serves as a vehicle for these materials and a medium for their changes; and excluding those mineral matters that play either passive or subsidiary parts; organisms are built up of compounds which are stores of force. Thus complex colloids and crystalloids which, as united together, form organized bodies, are the same colloids and crystalloids which give out, on their decomposition, the forces expended by organized bodies. Thus these nitrogenous and carbonaceous substances, being at once the materials for organic growth and the sources of organic energy, it results that as much of them as is used up for the genesis of energy is taken away from the means of growth, and as much as is economized by diminishing the genesis of energy, is available for growth. Given that limited quantity of nutritive matter which the pre-existing structure of an organism enables it to absorb; and it is a necessary corollary from the persistence of force, that the matter accumulated as growth cannot exceed that surplus which remains undecomposed after the production of the required amounts of sensible and insensible motion. This, which would be rigorously true under all conditions if exactly the same substances were used in exactly the same proportions for the production of force and for the formation of tissue, requires, however, to be taken with the qualification that some of the force-evolving substances are not constituents of tissue; and that thus there may be a genesis of force which is not at the expense of potential growth. But since organisms (or at least animal organisms, with which we are here chiefly concerned) have a certain power of selective absorption, which, partially in an individual and more completely in a race, adapts the proportions of the substances absorbed to the needs of the system; then if a certain habitual expenditure of force leads to a certain habitual absorption of force-evolving matters that are not available for growth; and if, were there less need for such matters, the ability to absorb matters available for growth would be increased to an equivalent extent; it follows that the antagonism described does, in the long run, hold even without this qualification. Hence, growth is substantially equivalent to the absorbed nutriment, minus the nutriment used up in action.

This, however, is no answer to the question—why has individual growth a limit?—why do the increments of growth bear decreasing ratios to the mass and finally come to an end? The question is involved. There are more causes than one why the excess of absorbed nutriment over expended nutriment must, other things equal, become less as the size of the animal becomes greater. In similarly-shaped bodies the masses, and therefore the weights, vary as the cubes of the dimensions; whereas the powers of bearing the stresses imposed by the weights vary as the squares of the dimensions. Suppose a creature which a year ago was one foot high, has now become two feet high, while it is unchanged in proportions and structure; what are the necessary concomitant changes? It is eight times as heavy; that is to say, it has to resist eight times the strain which gravitation puts upon certain of its parts; and when there occurs sudden arrest of motion or sudden genesis of motion, eight times the strain is put upon the muscles employed. Meanwhile the muscles and bones have severally increased their abilities to bear strains in proportion to the areas of their transverse sections, and hence have severally only four times the tenacity they had. This relative decrease in the power of bearing stress does not imply a relative decrease in the power of generating energy and moving the body; for in the case supposed the muscles have not only increased four times in their transverse sections but have become twice as long, and will therefore generate an amount of energy proportionate to their bulk. The implication is simply that each muscle has only half the power to withstand those shocks and strains which the creature's movements entail; and that consequently the creature must be either less able to bear these, or must have muscles and bones having relatively greater transverse dimensions: the result being that greater cost of nutrition is inevitably caused and therefore a correlative tendency to limit growth. This necessity will be seen still more clearly if we leave out the motor apparatus, and consider only the forces required and the means of supplying them. For since, in similar bodies, the areas vary as the squares of the dimensions, and the masses vary as the cubes; it follows that the absorbing surface has become four times as great, while the weight to be moved by the matter absorbed has become eight times as great. If then, a year ago, the absorbing surface could take up twice as much nutriment as was needed for expenditure, thus leaving one-half for growth, it is now able only just to meet expenditure, and can provide nothing for growth. However great the excess of assimilation over waste may be during the early life of an active organism, we see that because a series of numbers increasing as the cubes, overtakes a series increasing as the squares, even though starting from a much smaller number, there must be reached, if the organism lives long enough, a point at which the surplus assimilation is brought down to nothing—a point at which expenditure balances nutrition—a state of moving equilibrium. The only way in which the difficulty can be met is by gradual re-organization of the alimentary system; and, in the first place, this entails direct cost upon the organism, and, in the second place, indirect cost from the carrying of greater weight: both tending towards limitation. There are two other varying relations between degrees of growth and amounts of expended force; one of which conspires with the last, while the other conflicts with it. Consider, in the first place, the cost at which nutriment is distributed through the body and effete matters removed from it. Each increment of growth being added at the periphery of the organism, the force expended in the transfer of matter must increase in a rapid progression—a progression more rapid than that of the mass. But as the dynamic expense of distribution is small compared with the dynamic value of the materials distributed, this item in the calculation is unimportant. Now consider, in the second place, the changing proportion between production and loss of heat. In similar organisms the quantities of heat generated by similar actions going on throughout their substance, must increase as the masses, or as the cubes of the dimensions. Meanwhile, the surfaces from which loss of heat takes place, increase only as the squares of the dimensions. Though the loss of heat does not therefore increase only as the squares of the dimensions, it certainly increases at a smaller rate than the cubes. And to the extent that augmentation of mass results in a greater retention of heat, it effects an economization of force. This advantage is not, however, so important as at first appears. Organic heat is a concomitant of organic action, and is so abundantly produced during action that the loss of it is then usually of no consequence: indeed the loss is often not rapid enough to keep the supply from rising to an inconvenient excess. It is chiefly in respect of that maintenance of heat which is needful during quiescence, that large organisms have an advantage over small ones in this relatively diminished loss. Thus these two subsidiary relations between degrees of growth and amounts of expended force, being in antagonism, we may conclude that their differential result does not greatly modify the result of the chief relation.

Comparisons of these deductions with the facts appear in some cases to verify them and in other cases not to do so. Throughout the vegetal kingdom, there are no distinct limits to growth except those which death entails. Passing over a large proportion of plants which never exceed a comparatively small size, because they wholly or partially die down at the end of the year, and looking only at trees that annually send forth new shoots, even when their trunks are hollowed by decay; we may ask—How does growth happen here to be unlimited? The answer is, that plants are only accumulators: they are in no very appreciable degree expenders. As they do not undergo waste there is no reason why their growth should be arrested by the equilibration of assimilation and waste. Again, among animals there are sufficient reasons why the correspondence cannot be more than approximate. Besides the fact above noted, that there are other varying relations which complicate the chief one. We must bear in mind that the bodies compared are not truly similar: the proportions of trunk to limbs and trunk to head, vary considerably. The comparison is still more seriously vitiated by the inconstant ratio between the constituents of which the body is composed. In the flesh of adult mammalia, water forms from 68 to 71 per cent., organic substance from 24 to 28 per cent., and inorganic substance from 3 to 5 per cent.; whereas in the fœtal state, the water amounts to 87 per cent., and the solid organic constituents to only 11 per cent. Clearly this change from a state in which the force-evolving matter forms one-tenth of the whole, to a state in which it forms two and a half tenths, must greatly interfere with the parallelism between the actual and the theoretical progression. Yet another difficulty may come under notice. The crocodile is said to grow as long as it lives; and there appears reason to think that some predaceous fishes, such as the pike, do the same. That these animals of comparatively high organization have no definite limits of growth, is, however, an exceptional fact due to the exceptional non-fulfilment of those conditions which entail limitation. What kind of life does a crocodile lead? It is a cold-blooded, or almost cold-blooded, creature; that is, it expends very little for the maintenance of heat. It is habitually inert: not usually chasing prey but lying in wait for it; and undergoes considerable exertion only during its occasional brief contests with prey. Such other exertion as is, at intervals, needful for moving from place to place, is rendered small by the small difference between the animal's specific gravity and that of water. Thus the crocodile expends in muscular action an amount of force that is insignificant compared with the force commonly expended by land-animals. Hence its habitual assimilation is diminished much less than usual by habitual waste; and beginning with an excessive disproportion between the two, it is quite possible for the one never quite to lose its advance over the other while life continues. On looking closer into such cases as this and that of the pike, which is similarly cold-blooded, similarly lies in wait, and is similarly able to obtain larger and larger kinds of prey as it increases in size; we discover a further reason for this absence of a definite limit. To overcome gravitative force the creature has not to expend a muscular power that is large at the outset, and increases as the cubes of its dimensions: its dense medium supports it. The exceptional continuance of growth observed in creatures so circumstanced, is therefore perfectly explicable.

§ 46a. If we go back upon the conclusions set forth in the preceding section, we find that from some of them may be drawn instructive corollaries respecting the limiting sizes of creatures inhabiting different media. More especially I refer to those varying proportions between mass and stress from which, as we have seen, there results, along with increasing size, a diminishing power of mechanical self-support: a relation illustrated in its simplest form by the contrast between a dew-drop, which can retain its spheroidal form, and the spread-out mass of water which results when many dew-drops run together. The largest bird that flies (the argument excludes birds which do not fly) is the Condor, which reaches a weight of from 30 to 40 lbs. Why does there not exist a bird of the size of an elephant? Supposing its habits to be carnivorous, it would have many advantages in obtaining prey: mammals would be at its mercy. Evidently the reason is one which has been pointed out—the reason that while the weight to be raised and kept in the air by a bird increases as the cubes of its dimensions, the ability of its bones and muscles to resist the strains which flight necessitates, increases only as the squares of the dimensions. Though, could the muscles withstand any tensile strain they were subject to, the power like the weight might increase with the cubes, yet since the texture of muscle is such that beyond a certain strain it tears, it results that there is soon reached a size at which flight becomes impossible: the structures must give way. In a preceding paragraph the limit to the size of flying creatures was ascribed to the greater physiological cost of the energy required; but it seems probable that the mechanical obstacle here pointed out has a larger share in determining the limit.

In a kindred manner there results a limitation of growth in a land-animal, which does not exist for an animal living in the water. If, after comparing the agile movements of a dog with those of a cow, the great weight of which obviously prevents agility; or if, after observing the swaying flesh of an elephant as it walks along, we consider what would happen could there be formed a land-animal equal in mass to the whale (the long Dinosaurs were not proportionately massive) it needs no argument to show that such a creature could not stand, much less move about. But in the water the strain put upon its structures by the weights of its various parts is almost if not quite taken away. Probably limitation in the quantity of food obtainable becomes now the chief, if not the sole, restraint.

And here we may note, before leaving the topic, something like a converse influence which comes into play among creatures inhabiting the water. Up to the point at which muscles tear from over-strain, larger and smaller creatures otherwise alike, remain upon a par in respect of the relative amounts of energy they can evolve. Had they to encounter no resistance from their medium, the implication would be that neither would have an advantage over the other in respect of speed. But resistance of the medium comes into play; and this, other things equal, gives to the larger creature an advantage. It has been found, experimentally, that the forces to be overcome by vessels moving through the water, built as they are with immersed hinder parts which taper as fish taper, are mainly due to what is called "skin-friction." Now in two fish unlike in size but otherwise similar skin-friction bears to the energy that can be generated, a smaller proportion in the larger than in the smaller; and the larger can therefore acquire a greater velocity. Hence the reason why large fish, such as the shark, become possible. In a habitat where there is no ambush (save in exceptional cases like that of the Lophius or Angler) everything depends on speed; and if, other things equal, a larger fish had no mechanical advantage over a smaller, a larger fish could not exist—could not catch the requisite amount of prey.

§ 47. Obviously this antagonism between accumulation and expenditure, must be a leading cause of the contrasts in size between allied organisms that are in many respects similarly conditioned. The life followed by each kind of animal is one involving a certain average amount of exertion for the obtainment of a given amount of nutriment—an exertion, part of which goes to the gathering or catching of food, part to the tearing and mastication of it, and part to the after-processes requisite for separating the nutritive molecules—an exertion which therefore varies according as the food is abundant or scarce, fixed or moving, according as it is mechanically easy or difficult to deal with when secured, and according as it is, or is not, readily soluble. Hence, while among animals of the same species having the same mode of life, there will be a tolerably constant ratio between accumulation and expenditure, and therefore a tolerably constant limit of growth, there is every reason to expect that different species, following different modes of life, will have unlike ratios between accumulation and expenditure, and therefore unlike limits of growth.

Though the facts as inductively established, show a general harmony with this deduction, we cannot usually trace it in any specific way; since the conflicting and conspiring factors which affect growth are so numerous.

§ 48. One of the chief causes, if not the chief cause, of the differences between the sizes of organisms, has yet to be considered. We are introduced to it by pushing the above inquiry a little further. Small animals have been shown to possess an advantage over large ones in the greater ratio which, other things equal, assimilation bears to expenditure; and we have seen that hence small animals in becoming large ones, gradually lose that surplus of assimilative power which they had, and eventually cannot assimilate more than is required to balance waste. But how come these animals while young and small to have surplus assimilative powers? Have all animals equal surpluses of assimilative powers? And if not, how far do differences between the surpluses determine differences between the limits of growth? We shall find, in the answers to these questions, the interpretation of many marked contrasts in growth that are not due to any of the causes above assigned. For example, an ox immensely exceeds a sheep in mass. Yet the two live from generation to generation in the same fields, eat the same grass, obtain these aliments with the same small expenditure of energy, and differ scarcely at all in their degrees of organization. Whence arises, then, their striking unlikeness of bulk?

We noted when studying the phenomena of growth inductively, that organisms of the larger and higher types commence their separate existences as masses of organic matter having tolerable magnitudes. Speaking generally, we saw that throughout each organic sub-kingdom the acquirement of great bulk occurs only where the incipient bulk and organization are considerable; and that they are the more considerable in proportion to the complexity of the life which the organism is to lead.

The deductive interpretation of this induction may best be commenced by an analogy. A street orange-vendor makes but a trifling profit on each transaction; and unless more than ordinarily fortunate, he is unable to realize during the day a larger amount than will meet his wants; leaving him to start on the morrow in the same condition as before. The trade of the huxter in ounces of tea and half-pounds of sugar, is one similarly entailing much labour for small returns. Beginning with a capital of a few pounds, he cannot have a shop large enough, or goods sufficiently abundant and various, to permit an extensive business. He must be content with the half-pence and pence which he makes by little sales to poor people; and if, avoiding bad debts, he is able by strict economy to accumulate anything, it can be but a trifle. A large retail trader is obliged to lay out much money in fitting up an adequate establishment; he must invest a still greater sum in stock; and he must have a further floating capital to meet the charges that fall due before his returns come in. Setting out, however, with means enough for these purposes, he is able to make many and large sales; and so to get greater and more numerous increments of profit. Similarly, to get returns in thousands merchants and manufacturers must make their investments in tens of thousands. In brief, the rate at which a man's wealth accumulates is measured by the surplus of income over expenditure; and this, save in exceptionably favourable cases, is determined by the capital with which he begins business. Now applying the analogy, we may trace in the transactions of an organism, the same three ultimate elements. There is the expenditure required for the obtainment and digestion of food; there is the gross return in the shape of nutriment assimilated or fit for assimilation; and there is the difference between this gross return of nutriment and the nutriment that was used up in the labour of securing it—a difference which may be a profit or a loss. Clearly, however, a surplus implies that the force expended is less than the force latent in the assimilated food. Clearly, too, the increment of growth is limited to the amount of this surplus of income over expenditure; so that large growth implies both that the excess of nutrition over waste shall be relatively considerable, and that the waste and nutrition shall be on extensive scales. And clearly, the ability of an organism to expend largely and assimilate largely, so as to make a large surplus, presupposes a large physiological capital in the shape of organic matter more or less developed in its structural arrangements.

Throughout the vegetal kingdom, the illustrations of this truth are not conspicuous and regular: the obvious reason being that since plants are accumulators and in so small a degree expenders, the premises of the above argument are but very partially fulfilled. The food of plants (excepting Fungi and certain parasites) being in great measure the same for all, and bathing all so that it can be absorbed without effort, their vital processes result almost entirely in profit. Once fairly rooted in a fit place, a plant may thus from the outset add a very large proportion of its entire returns to capital; and may soon be able to carry on its processes on a large scale, though it does not at first do so. When, however, plants are expenders, namely, during their germination and first stages of growth, their degrees of growth are determined by their amounts of vital capital. It is because the young tree commences life with a ready-formed embryo and store of food sufficient to last for some time, that it is enabled to strike root and lift its head above the surrounding herbage. Throughout the animal kingdom, however, the necessity of this relation is everywhere obvious. The small carnivore preying on small herbivores, can increase in size only by small increments: its organization unfitting it to digest larger creatures, even if it can kill them, it cannot profit by amounts of nutriment exceeding a narrow limit; and its possible increments of growth being small to set out with, and rapidly decreasing, must come to an end before any considerable size is attained. Manifestly the young lion, born of tolerable bulk, suckled until much bigger, and fed until half-grown, is enabled by the power and organization which he thus gets gratis, to catch and kill animals big enough to give him the supply of nutriment needed to meet his large expenditure and yet leave a large surplus for growth. Thus, then, is explained the above-named contrast between the ox and the sheep. A calf and a lamb commence their physiological transactions on widely different scales; their first increments of growth are similarly contrasted in their amounts; and the two diminishing series of such increments end at similarly-contrasted limits.

§ 49. Such are the several conditions by which the phenomena of growth are determined. Conspiring and conflicting in endless unlike ways and degrees, they in every case qualify more or less differently each other's effects. Hence it happens that we are obliged to state each generalization as true on the average, or to make the proviso—other things equal.

Understood in this qualified form, our conclusions are these. First, that growth being an integration with the organism of such environing matters as are of like natures with the matters composing the organism, its growth is dependent on the available supply of them. Second, that the available supply of assimilable matter being the same, and other conditions not dissimilar, the degree of growth varies according to the surplus of nutrition over expenditure—a generalization which is illustrated in some of the broader contrasts between different divisions of organisms. Third, that in the same organism the surplus of nutrition over expenditure differs at different stages; and that growth is unlimited or has a definite limit, according as the surplus does or does not rapidly decrease. This proposition we found exemplified by the almost unceasing growth of organisms that expend relatively little energy; and by the definitely limited growth of organisms that expend much energy. Fourth, that among organisms which are large expenders of force, the size ultimately attained is, other things equal, determined by the initial size: in proof of which conclusion we have abundant facts, as well as the a priori necessity that the sum-totals of analogous diminishing series, must depend upon the amounts of their initial terms. Fifth, that where the likeness of other circumstances permits a comparison, the possible extent of growth depends on the degree of organization; an inference testified to by the larger forms among the various divisions and sub-divisions of organisms.