On Growth and Form

* These ‘‘Fezzan-worms,”’ when first described, were supposed to be “‘insects’ eges”; cf. Humboldt, Personal Narrative, vi, i, 8. note; Kirby and Spence. Letter x. t Cf. Abonyi, Z. f. w. Z. oxtv, p. 134, 1915. But Frédéricq has shewn that the amount of NaCl in the blood of Crustacea (Carcinus moenas) varies, and all but corres onds, with the density of the water in which the creature has been kept (Arch. de Zool. Exp. et Gén. (2), U1, p. xxxv, 1885); and other results of Frédéricq’s, and various data given or quoted by Bottazzi (Osmotischer Druck und elektrische Leitungsfihigkeit der Fliissigkeiten der Organismen, in Asher-Spiro’s Ergebn. d. Physiologie, vit, pp. 160-402, 1908) suggest that the case of the brine-shrimps must be looked upon as an extreme or exceptional one.

described as the specific characters of A. milhausenni, and of a still more extreme form, A. képpeniana; while on the other hand, progressive dilution of the water tends to precisely opposite conditions, resulting in forms which have also been described as separate species, and even referred to a separate genus, Callaonella, closely akin to Branchipus (Fig. 33). Pari passu with these changes, there is a marked change in the relative lengths of the fore and hind portions of the body, that is to say, of the “cephalothorax” and abdomen: the latter growing relatively longer, the salter the water. In other words, not only is the rate of growth of the whole

Fig. 33. Brine-shrimps (Artemia), from more or less saline water. Upper figures shew tail-segment and tail-fins; lower figures, relative length of cephalothorax and abdomen. (After Abonyi.) animal lessened by the saline concentration, but the specific rates of growth in the parts of its body are relatively changed. This latter phenomenon lends itself to numerical statement, and Abonyi has lately shewn that we may construct a very regular curve, by plotting the proportionate length of the creature’s abdomen against the salinity, or density, of the water; and the several species of Artemia, with all their other correlated specific characters, are then found to occupy successive, more or less well-defined, and more or less extended, regions of the curve (Fig. 33). In short, the density of the water is so clearly a “function” of the specific

character, that we may briefly define the species Artemia (Callaonella) Jelskw, for instance, as the Artemia of density 1000-1010 (NaCl), or the typical A. salina, or principalis, as the Artemia of density 1018-1025, and so forth. It is a most interesting fact that these Artemiae, under the protection of their semipermeable skins, are capable of living in waters not only of great density, but of very varied chemical composition. The natron-lakes, for instance, contain large quantities of magnesium

Fig. 34. Percentage ratio of length of abdomen to cephalothorax in brine-shrimps, at various salinities. (After Abonyi.) sulphate; and the Artemiae continue to live equally well in artificial solutions where this salt, or where calcium chloride, has largely taken the place of sodium chloride in the more common habitat. Furthermore, such waters as those of the natron-lakes are subject to very great changes of chemical composition as concentration proceeds, owing to the different solubilities of the constituent salts. It appears that the forms which the Artemiae assume, and the changes which they undergo, are identical or

indistinguishable, whichever of the above salts happen to exist, or to predominate, in their saline habitat. At the same time we still lack (so far as I know) the simple, but crucial experiments which shall tell us whether, in solutions of different chemical composition, it is at equal densities, or at “isotonic” concentrations (that is to say, under conditions where the osmotic pressure, and consequently the rate of diffusion, is identical), that the same structural changes are produced, or corresponding phases of equilibrium attained.

While Hoéber and others* have referred all these phenomena to osmosis, Abonyi is inclined to believe that the viscosity, or mechanical resistance, of the fluid also reacts upon the organism ; and other possible modes of operation havé been suggested. But we may take it for certain that the phenomenon as a whole is not a simple one; and that it includes besides the passive phenomena of intermolecular diffusion, some other form of activity which plays the part of a regulatory mechanismy.

In ordinary chemical reactions we have to deal (1) with a specific velocity proper to the particular reaction, (2) with variations due to temperature and other physical conditions, (3) according to van’t Hofi’s ‘‘ Law of Mass,’’ with variations due to the actual quantities present of the reacting substances, and (4) in certain cases, with variations due to the presence of “catalysing agents.” In the simpler reactions, the law of mass involves a steady, gradual slowing-down of the process, according to a logarithmic ratio, as the reaction proceeds and as the initial amount of substance diminishes; a phenomenon, however, which need not necessarily

+ According to the empirical canon of physiology, that (as Frédéricq expresses it) “L’étre vivant est agencé de telle maniere que chaque influence perturbatrice provoque d’elle-méme la mise en activité de Vappareil compensateur qui doit neutraliser et réparer le dommage.” occur in the organism, part of whose energies are devoted to the continual bringing-up of fresh supplies. Catalytic action occurs when some substance, often in very minute quantity, is present, and by its presence produces or accelerates an action, by opening ‘‘a way round,” without the catalytic agent itself being diminished or used up%*. Here the velocity curve, though quickened, is not necessarily altered in form, for gradually the law of mass exerts its effect and the rate of the reaction gradually diminishes. But in certain cases we have the very remarkable phenomenon that a body acting as a catalyser is necessarily formed as a product, or bye-product, of the main reaction, and in such a case as this the reaction-velocity will tend to be steadily accelerated. Instead of dwinding away, the reaction will continue with an everincreasing velocity: always subject to the reservation that limiting conditions will in time make themselves felt, such as a failure of some necessary ingredient, or a development of some substance which shall antagonise or finally destroy the original reaction. Such an action as this we have learned, from Ostwald, to describe as “autocatalysis.” Now we know that certain products of protoplasmic metabolism, such as the enzymes, are very powerful catalysers, and we are entitled to speak of an autocatalytic action on the part of protoplasm itself. This catalytic activity of protoplasm is a very important phenomenon. As Blackman says, in the address already quoted, the botanists (or the zoologists) “eall it growth, attribute it to a specific power of protoplasm for assimilation, anid leave it alone as a fundamental phenomenon ; but they are much concerned as to the distribution of new growth in innumerable specifically distinct forms.” While the chemist, on the other hand, recognises it as a familiar phenomenon, and refers it to the same category as his other known examples of autocatalysis.

* Such phenomena come precisely under the head of what Bacon called Instances of Magic: ‘ By which I mean those wherein the material or efficient cause is scanty and small as compared with the work or effect produced; so that even when they are common, they seem like miracles, some at first sight, others even after attentive consideration. These magical effects are brought about in three ways...[of which one is] by excitation or invitation in another body, as in the magnet which excites numberless needles without losing any of its virtue, or an yeast and such-like.’ Nov. Org., cap. li.

This very important, and perhaps even fundamental phenomenon of growth would seem to have been first recognised by Professor Chodat of Geneva, as we are told by his pupil Monnier *. “On peut bien, ainsi que M. Chodat l’a proposé, considérer Paccroissement comme une réaction chimique complexe, dans laquelle le catalysateur est la cellule vivante, et les corps en présence sont l’eau, les sels, et acide carbonique.” Very soon afterwards a similar suggestion was made by Loebt, in Gonnection with the synthesis of nuclein or nuclear protoplasm ; for he remarked that, as in an autocatalysed chemical reaction, the velocity of the synthesis increases during the initial stage of cell-division in proportion to the amount of nuclear matter already synthesised. In other words, one of the products of the reaction, i.e. one of the constituents of the ‘nucleus, accelerates the production of nuclear from cytoplasmic material.

The phenomenon of autocatalysis is by no means confined to hving or protoplasmic chemistry, but at the same time it is characteristically, and apparently constantly, associated therewith. And it would seem that to it we may ascribe a considerable part of the difference between the growth of the organism and the simpler growth of the crystal{: the fact, for instance, that the cell can grow in a very low concentration of its nutritive solution, while the crystal grows only in a supersaturated one; and the fundamental fact that the nutritive solution need only contain the more or less raw materials of the complex constituents of the cell, while the crystal grows only in a solution of its own actual substance §.

As F. F. Blackman has pointed out, the multiplication of an organism, for instance the prodigiously rapid increase of a bacterium, * Monnier, A., Les matiéres minérales, et la loi d’accroissement des Végétaux, Publ. de VInst. de Bot. de VUniv. de Genéve (7), 1, 1905. Cf. Robertson, On the Normal Rate of Growth of an Individual, and its Biochemical Significance, Arch. f. Entw. Mech. xxv, pp. 581-614, xxvi, pp. 108-118, 1908; Wolfgang Ostwald, Die zeitlichen Eigenschaften der Entwickelungsvorgdnge, 1908; Hatai, 8., Interpretation of Growth-curves from a Dynamical Standpoint, Anat. Record, v, p. 373,

{ Even a crystal may be said, in a sense, to display “autocatalysis”: for the bigger its surface becomes, the more rapidly does the mass go on increasing. which tends to double its numbers every few minutes, till (were it not for limiting factors) its numbers would be all but incalculable in a day*,is a simple but most striking illustration of the potentialities of protoplasmic catalysis; and (apart from the large share taken by mere “turgescence” or imbibition of water) the same is true of the growth, or cell-multiplication, of a multicellular organism in its first stage of rapid acceleration.

It is not necessary for us to pursue this subject much further, for it is sufficiently clear that the normal “curve of growth” of an organism, in all its general features, very closely resembles the velocity-curve of chemical autocatalysis. We see in it the first and most typical phase of greater and greater acceleration; this is followed by a phase in which limiting conditions (whose details are practically unknown) lead to a falling off of the former acceleration; and in most cases we come at length to a third phase, in which retardation of growth is succeeded by actual diminution of mass. Here we may recognise the influence of processes, or of products, which have become actually deleterious; their deleterious influence is staved off for awhile, as the organism draws on its accumulated reserves, but they lead ere long to the stoppage of all activity, and to the physical phenomenon of death. But when we have once admitted that the limiting conditions of growth, which cause a phase of retardation to follow a phase of acceleration, are very imperfectly known, it is plain that, ipso facto, we must admit that a resemblance rather than an identity between this phenomenon and that of chemical autocatalysis is all that we can safely assert meanwhile. Indeed, as Enriques has shewn, points of contrast between the two phenomena are not lacking; for instance, as the chemical reaction draws to a close, it is by the gradual attainment of chemical equilibrium: but when organic growth draws to a close, it is by reason of a very different kind of equilibrium, due in the main to the gradual differentiation of the organism into parts, among whose peculiar

* B. coli-communis, according to Buchner, tends to double in 22 minutes; in 24 hours, therefore, a single individual would be multiplied by something like 10°8; Sitzungsher. Miinchen. Ges. Morphol. u. Physiol. ut, pp. 65-71, 1888. Cf. Marshall Ward, Biology of Bacillus ramosus, etc. Pr. R. S. uvim, 265-468, 1895. The comparatively large infusorian Stylonichia, according to Maupas, would multiply in a month by 10%. and specialised functions that of cell-multiplication tends to fall into abeyance*.

It would seem to follow, as a natural consequence, from what has been said, that we could without much difficulty reduce our curves of growth to logarithmic formulae} akin to those which the physical chemist finds applicable to his autocatalytic reactions. This has been diligently attempted by various writers{; but the results, while not destructive of the hypothesis itself, are only partially successful. The difficulty arises mainly from the fact that, in the life-history of an organism, we have usually to deal (as indeed we have seen) with several recurrent periods of relative acceleration and retardation. It is easy to find a formula which shall satisfy the conditions during any one of these periodic phases, but it is very difficult to frame a comprehensive formula which shall apply to the entire period of growth, or to the whole duration of life.

But if it be meanwhile impossible to formulate or to solve in precise mathematical terms the equation to the growth of an organism, we have yet gone a very long way towards the solution . of such problems when we have found a “qualitative expression,” as Poincaré puts it; that is to say, when we have gained a fair approximate knowledge of the general curve which represents the unknown function. As soon as we have touched on such matters as the chemical phenomenon of catalysis, we are on the threshold of a subject which, if we were able to: pursue it, would soon lead us far into the special domain of physiology; and there it would be necessary to follow it if we were dealing with growth as a phenomenon in itself, instead of merely as a help to our study and comprehension of form. For instance the whole question of diet, of overfeeding and underfeeding, would present itself for discussion§. But without attempting to open up this large subject, we may say a

* Cf. Enriques, Wachsthum und seine analytische Darstellung, Biol. Centralbl. 1909, p. 337. § See, for a brief resumé of this subject, Morgan’s Haperimental Zoology, chap. Xvi. further passing word upon the essential fact that certain chemical substances have the power of accelerating or of retarding, or in some way regulating, growth, and of so influencing directly the morphological features of the organism. Thus lecithin has been shewn by Hatai*, Danilewsky} and others to have a remarkable power of stimulating growth in various animals; and the so-called “auximones,” which Professor Bottomley prepares by the action of bacteria upon peat appear to be, after a somewhat similar fashion, potent accelerators of the growth of plants. But by much the most interesting cases, from our point of view, are those where a particular substance appears to exert a differential effect, stimulating the growth of one part or organ of the body more than another.

It has been known for a number of years that a diseased condition of the pituitary body accompanies the phenomenon known as “acromegaly,” in which the bones are variously enlarged or elongated, and which is more or less exemplified in every skeleton of a “giant”; while on the other hand, disease or extirpation of the thyroid causes an arrest of skeletal development, and, if it take place early, the subject remains a dwarf. These, then, are well-known illustrations of the regulation of function by some internal glandular secretion, some enzyme or “hormone” (as Bayliss and Starling call it), or “harmozone,” as Gley calls it in the particular case where the function regulated is that of growth, with its consequent influence on form.

Among other illustrations (which are plentiful) we have, for instance the growth of the placental decidua, which Loeb has shewn to be due to a substance given off by the corpus luteum of the ovary, giving to the uterine tissues an abnormal capacity for growth, which in turn is called into action by the contact of the ovum, or even of any foreign body. And various sexual characters, such as the plumage, comb and spurs of the cock, are believed in like manner to arise in response to some particular internal secretion. When the source of such a secretion is removed by castration, well-known morphological changes take place in various animals; and when a converse change takes place, the female acquires, in greater or less degree, characters which are

proper to the male, as in certain extreme cases, known from time immemorial, when late in life a hen assumes the plumage of the cock. There are some very remarkable experiments by Gudernatsch, ~in which he has shewn that by feeding tadpoles (whether of frogs or toads) on thyroid gland substance, their legs may be made to grow out at any time, days or weeks before the normal date of their appearance*. No other organic food was found to produce the same effect; but since the thyroid gland is known to contain iodine +, Morse experimented with this latter substance, and found that if the tadpoles were fed with iodised amino-acids the legs developed precociously, just as when the thyroid gland itself was used. We may take it, then, as an established fact, whose full extent and bearings are still awaiting investigation, that there exist substances both within and without the organism which have a marvellous power of accelerating growth, and of doing so in such a way as to affect not only the size but the form or proportions of the organism.

If we once admit, as we are now bound to do, the existence of such factors as these, which, by their physiological activity and apart from any direct action of the nervous system, tend towards the acceleration of growth and consequent modification of form, we are led into wide fields of speculation by an easy and a legitimate pathway. Professor Gley carries such speculations a long, long way: for he sayst that by these chemical influences “Toute une partie de la construction des étres parait s expliquer dune facon toute mécanique. La forteresse, si longtemps inaccessible, du vitalisme est entamée. Car la notion morphogénique était, suivant le mot de Dastre§$, comme ‘le dernier réduit de la force vitale.’”

The physiological speculations we need not discuss: but, to take a single example from morphology, we begin to understand the possibility, and to comprehend the probable meaning, of the + Cf. Baumann u. Roos, Vorkommen von Iod im Thierkérper, Zeitschr. fiir Physiol. Chem. Xx1, xxut, 1895, 6. all but sudden appearance on the earth of such exaggerated and almost monstrous forms as those of the great secondary reptiles and the great tertiary mammals*. We begin to see that it is in order to account, not for the appearance, but for the disappearance of such forms as these that natural selection must be invoked. And we then, I think, draw near to the conclusion that what is true of these is universally true, and that the great function of natural selection is not to originate, but to remove: donec ad interitum genus id natura redegitt.

The world of things living, like the world of things inanimate, grows of itself, and pursues its ceaseless course of creative evolution. It has room, wide but not unbounded, for variety of living form and structure, as these tend towards their seemingly endless, but yet strictly limited, possibilities of permutation and degree: it has room for the great and for the small, room for the weak and for the strong: Environment and circumstance do not always ' make a prison, wherein perforce the organism must either live or die; for the ways of life may be changed, and many a refuge found, before the sentence of unfitness is pronounced and the penalty of extermination paid. But there comes a time when “variation, in form, dimensions, or other qualities of the organism, goes farther than is compatible with all the means at hand of health and welfare for the individual and the stock; when, under the active and creative stimulus of forces from within and from without, the active and creative energies of growth pass the bounds of physical and physiological equilibrium: and so reach the limits which, as again Lucretius tells us, natural law has set between what may and what may not be,

“et quid quaeque queant per foedera naturai quid porro nequeant.” Then, at last, we are entitled to use the customary metaphor, and to see in natural selection an inexorable force, whose function + Lucret. v. 877. “Lucretius nowhere seems to recognise the possibility of improvement or change of species by ‘natural selection’; the animals remain as they were at the first, except that the weaker and more useless kinds have been crushed out. Hence he stands in marked contrast with modern evolutionists.” Kelsey’s note, ad loc.

is not to create but to destroy,—to weed, to prune, to cut down and to cast into the fire*. The phenomenon of regeneration, or the restoration of lost or amputated parts, is a particular case of growth which deserves separate consideration.. As we are all aware, this property is manifested in a high degree among invertebrates and many coldblooded vertebrates, diminishing as we ascend the scale, until at length, in the warm-blooded animals, it lessens down to no more than that vis medicatricx which heals a wound. Ever since the days of Aristotle, and especially since the experiments of Trembley, Réaumur and Spallanzani in the middle of the eighteenth century, the physiologist and the psychologist have alike recognised that ‘the phenomenon is both perplexing and important. The general phenomenon is amply discussed elsewhere, and we need, only deal with it in its immediate relation to growthf.

Regeneration, like growth in other cases, proceeds with a velocity which varies according to a definite law; the rate varies with the time, and we may study it as velocity and as acceleration. Let us take, as an instance, Miss M. L. Durbin’s measurements of the rate of regeneration of tadpoles’ tails: the rate being here measured in terms, not of mass, but of length, or longitudinal increment {. From a number of tadpoles, whose average length was 34-2 mm., their tails being on an average 21-2 mm. long, about half the tail

* Even after we have so narrowed the scope and sphere of natural selection, it is still hard to understand; for the causes of extinction are often wellnigh as hard ~ to comprehend as are those of the origin of species. If we assert (as has been lightly done) that Smilodon perished owing to its gigantic tusks, that Teleosaurus was handicapped by its exaggerated snout, or Stegosaurus weighed down by its intolerable load of armour, we may be reminded of other kindred forms to show that similar conditions did not necessarily lead to extermination, or that rapid extinction ensued apart from any such visible or apparent disadvantages. Cf. Lucas, F. A., On Momentum in Variation, Amer. Nat. xli, p. 46, 1907.

+ See Professor T. H. Morgan’s Regeneration (316 pp.), 1901 for a full account and copious bibliography. The early experiments on regeneration, by Vallisneri, Réaumur, Bonnet, Trembley, Baster, and others, are epitomised by Haller, Elem. Physioloyiae, vat, p. 156 seq. (11-5 mm.) was cut off, and the amounts regenerated in successive periods are shewn as follows: The first line of numbers in this table, if plotted as a curve against the number of days, will give us a very satisfactory view of the “curve of growth” within the period of the observations: that is to say, of the successive relations of length to time, or the velocity of the process. But the third line is not so satisfactory, and must not be plotted directly as an acceleration curve. For it is evident that the “rates” here determined do not correspond to velocities at the dates to which they are referred, but are the mean velocities over a preceding period; and moreover the periods over which these means are taken are liere of very unequal length. But we may draw a good deal more information from this experiment, if we begin by drawing a smooth curve, as nearly as possible through the points corresponding to the amounts regenerated (according to the first line of the table); and if we then interpolate from this smooth curve the actual lengths attained, day by day, and derive from these, by subtraction, the successive daily increments, which are the measure of the daily mean velocities (Table, p. 141). (The more accurate and strictly correct method would be to draw successive tangents to the curve.)