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.