On Growth and Form

Correlation of Stature and Increment in Boys and Girls. (From Boas and Wissler.) A minor, but very curious point brought out by the same investigators is that, if instead of stature we deal with height in the sitting posture (or, practically speaking, with length of trunk or back), then the correlations between this height and its annual increment are throughout negative. In other words, there would seem to be a general tendency for the long trunks to grow slowly throughout the whole period under investigation. It is a well-known anatomical fact that tallness is in the main due not to length of body but to length of limb.

The whole phenomenon of variability in regard to magnitude and to rate of increment is in the highest degree suggestive: inasmuch as it helps further to remind and to impress upon us that specific rate of growth is the real physiological factor which we want to get at, of which specific magnitude, dimensions and form, and all the variations of these, are merely the concrete and visible resultant. But the problems of variability, though they are intimately related to the general problem of growth, carry us very soon beyond our present limitations.

Just as the human curve of growth has its shght but wellmarked interruptions, or variations in rate, coinciding with such epochs as birth and puberty, so is it with other animals, and this phenomenon is particularly striking in the case of animals which undergo a regular metamorphosis. In the accompanying curve of growth in weight of the mouse (Fig. 12), based on W. Ostwald’s observations}, we see a distinct slackening of the rate when the mouse is about a fortnight old, at which period it opens its eyes and very soon afterwards is weaned. At about six weeks old there is «nother well-marked retardation of growth, following on a very rapid period, and coinciding with the epoch of puberty.

* See, for an admirable résumé of facts, Wolfgang Ostwald, Ueber die Zeitliche Eigenschaften der Entwickelungsvorgdnge (71 pp.), Leipzig, 1908 (Roux’s Vortrdge, Heft v): to which work I am much indebted. A long list of observations on the growth-rate of various animals is also given by H. Przibram, Hap. Zoologie, 1913, pt 1v (Vitalitat), pp. 85-87. Fig. 13 shews the curve of growth of the silkworm*, during its whole lary | life, up to the time of its entering the chrysalis stage.

The silkworm moults four times, at intervals of about a week, the first moult being on the sixth or seventh day after hatching. A distinct retardation of growth is exhibited on our curve in the case of the third and fourth moults; while a similar retardation accompanies the first and second moults also, but the scale of our diagram does not render it visible. When the worm is about seven weeks old, a remarkable process of “ purgation” takes place,

as a preliminary ‘to entering on the pupal, or chrysalis, stage ; and the great and sudden loss of weight which accompanies this process is the most marked feature of our curve. The rate of growth in the tadpole t (Fig. 14) is likewise marked by epochs of retardation, and finally by a sudden and drastic change. There is a slight diminution in weight immediately after the little larva frees itself from the egg; there is a retardation of growth about ten days later, when the external gills disappear ; and finally, the complete metamorphosis, with the loss of the tail,

Fig. 13 Growth in weight of Silkworm. (From Ostwald, after Luciani and Lo Monaco.) the growth of the legs and the cessation of branchial respiration, is accompanied by a loss of weight amounting to wellnigh half the weight of the full-grown larva. While as a general rule, the better the animals be fed the quicker they grow and the sooner they metamorphose, Barfiirth has pointed out the curious fact that a short spell of starvation, just before metamorphosis is due, appears to hasten the change.

Fig. 14. Growth in weight of Tadpole. (From Ostwald, after Schaper.) The negative growth, or actual loss of bulk and weight which often, and perhaps always, accompanies metamorphosis, is well shewn in the case of the eel*. The contrast of size is great between * Joh. Schmidt, Contributions to the Life-history of the Eel, Rapports du Conseil Intern. pour V exploration de la Mer, vol. v, pp. 137-274, Copenhague, 1906. Fig. 15. Development of Eel; from Leptocephalus larvae to young Elver. (From Ostwald after Joh. Schmidt.)

the flattened, lancet-shaped Leptocephalus larva and the little black cylindrical, almost thread-like elver, whose magnitude is less than that of the Leptocephalus in every dimension, even, at first, in length (Fig. 15). From the higher study of the physiology of growth we learn that such fluctuations as we have described are but special interruptions in a process which is never actually continuous, but is perpetually interrupted in a rhythmic manner*. Hofmeister shewed, for instance, that the growth of Spirogyra proceeds by fits and starts, by periods of activity and rest, which alternate with one another at intervals of so many minutes (Fig. 16). And

Fig. 16. Growth in length of Spirogyra. (From Ostwald, after Hofmeister.) Bose, by very refined methods of experiment, has shewn that plant-growth really proceeds by tiny and perfectly rhythmical pulsations recurring at regular intervals of a few seconds of time. Fig. 17 shews, according to Bose’s observations}, the growth of a crocus, under a very high magnification. The stalk grows by little jerks, each with an amplitude of about -002 mm., every

* That the metamorphoses cf an insect are but phases in a process of growth, was firstly clearly recognised by Swammerdam, Biblia Naturae, 1737, pp. 6, 579 ete. twenty seconds or so, and after each little increment there is a partial recoil. Fig. 17. Pulsations of growth in Crocus. in micro-millimetres. (After Bose.) The differences in regard to rate of growth between various parts or organs of the body, internal and external, can be amply illustrated in the case of man, and also, but chiefly in regard to external form, in some few other creatures}. It is obvious that there lies herein an endless field for the mathematical study of correlation and of variability, but with this aspect of the case we cannot deal.

In the accompanying table, I shew, from some of Vierordt’s data, the relative weights, at various ages, compared with the weight at birth, of the entire body, of the brain, heart and liver; * This phenomenon, of incrementum inequale, as opposed to incrementum in universum, was most carefully studied by Haller: “Incrementum inequale multis modis fit, ut aliae partes corporis aliis celerius increscant. Diximus hepar minus fieri, majorem pulmonem, minimum thymum, etc.” (Hlem. vim (2), p. 34).

7 See (inter alia) Fischel, A., Variabilitaét und Wachsthum des embryonalen Korpers, Morphol. Jahrb. xxtv. pp. 369-404, 1896. Oppel, Vergleichung des Entwickelungsgrades der Organe zu verschiedenen Entwickelungszeiten bei Wirbelthieren, Jena, 1891. Faucon, A., Pesées et Mensurations fetales a différents dges de la grossesse. (These.) Paris, 1897. Loisel, G., Croissance comparée en poids et en longueur des foetus male et femelle dans l’espece humaine, C. R. Soc. de Biologie, Paris, 1903. Jackson, C. M., Pre-natal growth of the human body and the relative growth of the various organs and parts, Am. J. of Anat. rx, 1909; Post-natal growth and variability of the body and of the various organs in the albino rat, zbid. xv, 1913.

and also the percentage relation which each of these organs bears, at the several ages, to the weight of the whole body. Weight of Various Organs, compared with the Total Weight of the Human Body (male). (After Vierordt, Anatom. Tabellen, pp. 38, 39.) From the first portion of the table, it will be seen that none of these organs by any means keep pace with the body as a whole in regard to growth in weight; in other words, there must be ‘some other part of the fabric, doubtless the muscles and the bones, which increase more rapidly than the average increase of the body. Heart and liver both grow nearly at the same rate, and by the

age of twenty-five they have multiplied their weight at birth by about thirteen times, while the weight of the entire body has been multiplied by about twenty-one; but the weight of the brain has meanwhile been multiplied only about three and a quarter times. In the next place, we see the very remarkable phenomenon that the brain, growing rapidly till the child is about four years old, then grows more much slowly till about eight or nine years old, and after that time there is scarcely any further perceptible increase. These phenomena are diagrammatically illustrated in Fig. 18.

Many statistics mdicate a decrease of brain-weight during adult life- Boas* was inclined to attribute this apparent phenomenon to our statistical methods, and to hold that it could ‘‘hardly be explained in any other way than by assuming an increased death-rate among men with very large brains, at an age of about twenty years.’’ But Raymond Pearl has shewn that there is evidence of a steady and very gradual decline in the weight of the brain with advancing age, beginning at or before the twentieth year, and continuing throughout adult lifey.

The second part of the table shews the steadily decreasing weights of the organs in question as compared with the body; the brain falling from over 12 per cent. at birth to little over 2 per cent. at five and twenty; the heart from -75 to :46 per cent.; and the liver from 4:57 to 2:75 per cent. of the whole bodily weight. It is plain, then, that there is no simple and direct relation, holding good throughout life, between the size of the body as a whole and that of the organs we have just discussed; and the changing ratio of magnitude is especially marked in the case of the brain, which, as we have just seen, constitutes about one-eighth of the whole bodily weight at birth, and but one-fiftieth at five and twenty. The same change of ratio is observed in other animals, in equal or even greater degree. For instance, Max Weber* tells us that in the lion, at five weeks, four months, eleven months, and lastly when full-grown, the brain-weight represents the following fractions of the weight of the whole body, viz. 1/18, 1/80, 1/184, and 1/546. And Kellicott has, in like manner, shewn that in the dogfish, while some organs (e.g. rectal gland, pancreas, etc.) increase steadily and very nearly proportionately to the body as a whole, the brain, and some other organs also, grow in a diminishing ratio, which is capable of representation, approximately, by a logarithmic curvef.

But if we confine ourselves to the adult, then, as Raymond Pearl has shewn in the case of man, the relation of brain-weight to age, to stature, or to weight, becomes a comparatively simple one, and may be sensibly expressed by a straight line, or simple equation. Thus, if W be the brain-weight (in grammes), and A be the age, or S the stature, of the individual, then (in the case of Swedish males) the following simple equations suffice to give the required ratios :

+ Amer. J. of Anatomy, vu, pp. 319-353, 1908. Donaldson (Journ. Comp. Neur. and Psychol. xvm, pp. 345-392, 1908) also gives a logarithmic formula for brain-weight (y) as compared with body-weight (a), which in the case of the white rat is y = 554 + -569 log (w— 8-7), and the agreement is very close. But the formula 1s admittedly empirica and as Raymond Pearl says (Amer. Nat. 1909, p. 303), ‘‘ no ulterior biological significance is to be attached to it.”

These equations are applicable to ages between fifteen and eighty ; if we take narrower limits, say between fifteen and fifty, we can get a closer agreement by using somewhat altered constants. In the two sexes, and in different races, these empirical constants will be greatly changed*. Donaldson has further shewn that the correlation between brain-weight and body-weight is very much closer — in the rat than in manf. The falling ratio of weight of brain to body with increase of size or age finds its parallel in comparative anatomy, in the general law that the larger the animal the less is the relative weight of the brain.

For much information on this subject, see Dubois, ‘‘ Abhaingigkeit des Hirngewichtes von der Kérpergrésse bei den Saugethieren,” Arch. f. Anthropol. xxv, 1897. Dubois has attempted, but I think with very doubtful success, to equate the weight of the brain with that of the animal. We may do this, in a very simple way, by representing the weight of the body as a power of that of the brain; thus, in the above table of the weights of brain and body in four species of cat, if we call W the weight of the body (in grammes), and w the weight of the brain, then if in all four cases we express the ratio by W = w", we find that » is almost constant, and differs little from 2-24 in all four species: the values being respectively, in the order of the table 2-36, 2-24, 2:18, and 2-17. But this evidently amounts to no more than an empirical rule; for we can easily see that it depends on the particular scale which we have used, and that if the weights had been taken, for instance, in kilogrammes or in milligrammes, the agreement or coincidence would not have occurred ¢.

+ Donaldson, H. H., A Comparison of the White Rat with Man in respect to the Growth of the entire Body, Boas Memorial Vol., New York, 1906, pp. 5-26. t Besides many papers quoted by Dubois on the growth and weight of the brain, and numerous papers in Biometrika, see also the following: Ziehen, Th., Das Gehirn: Massverhdltnisse, in Bardeleben’s Handb. der Anat. des Menschen, Iv, pp. 353-386, 1899. Spitzka, E. A., Brain-weight of Animals with special reference to the Weight of the Brain in the Macaque Monkey, J. Comp. Neurol.

The Length of the Head in Man at various Ages. (After Quetelet, p. 207.) Men Women Age Total height Head Ratio Height Head* Ratio m. m m m * A smooth curve, very similar to this, for the growth in “auricular height” of the girl’s head, is given by Pearson, in Biometrika, 11, p. 141. 1904. As regards external form, very similar differences exist, which however we must express in terms not of weight but of length. Thus the annexed table shews the changing ratios of the vertical length of the head to the entire stature; and while this ratio constantly diminishes, it will be seen that the rate of change is greatest (or the coefficient of acceleration highest) between the ages of about two and five years.

In one of Quetelet’s tables (swpra, p. 63), he gives measurements of the total span of the outstretched arms in man, from year to year, compared with the vertical stature. The two measurements are so nearly identical in actual magnitude that a direct comparison by means of curves becomes unsatisfactory ; but I have reduced Quetelet’s data to percentages, and it will be seen from Fig. 19 that the percentage proportion of span to height undergoes a remarkable and steady change from birth to the age of twenty years; the man grows more rapidly in stretch

of-arms than he does in height, and the span which was less than xm, pp. 9-17, 1903. Warneke, P., Mitteilung neuer Gehirn und Ké6rpergewichtsbestimmungen bei Saugern, nebst Zusammenstellung der gesammten bisher beobachteten absoluten und relativen Gehirngewichte bei den verschiedenen Species, J. f. Psychol. u. Neurol. xm, pp. 355-403, 1909. Donaldson, H. H., On the regular seasonal Changes in the relative Weight of the Central Nervous System ofthe Leopard Frog, Journ. of Morph. xxtt, pp. 663-694, 1911.

the stature at birth by about 1 per cent. exceeds it at the age of twenty by about 4 per cent. After the age of twenty, Quetelet’s data are few and irregular, but it is clear that the span goes on for a long while increasing in proportion to the stature. How far the phenomenon is due to actual growth of the arms and how far to the increasing breadth of the chest is not yet: ascertained. Fig. 19. Ratio of stature in Man, to span of outstretched arms. (From Quetelet’s data.)

The differences of rate of growth in different parts of the body are very simply brought out by the following table, which shews the relative growth of certain parts and organs of a young trout, at intervals of a few days during the period of most rapid development. It would not be difficult, from a picture of the little trout at any one of these stages, to draw its approximate form at any other, by the help of the numerical data here set forth*.

Trout (Salmo fario): proportionate growth of various organs. (From Jenkinson’s data.) Days Total Ist - Ventral 2nd Breadth old. length Kye Head dorsal fin dorsal ‘Tail-fin of tail While it is inequality of growth in different directions that we can most easily comprehend as a phenomenon leading to gradual change of outward form, we shall see in another chapter* that differences of rate at different parts of a longitudinal system, though always in the same direction, also lead to very notable and regular transformations. Of this phenomenon, the difference in rate of longitudinal growth between head and body is a simple case, and the difference which accompanies and results from it in the bodily form of the child and the man is easy to see. A like phenomenon has been studied in much greater detail in the case of plants, by Sachs and certain other botanists, after a method in use by Stephen Hales a hundred and fifty years before.

On the growing root of a bean, ten narrow zones were marked off, starting from the apex, each zone a millimetre in breadth. After twenty-four hours’ growth, at a certain constant temperature, the whole marked portion had grown from 10 mm. to 33 mm. in length; but the individual zones had grown at very unequal rates, as shewn in the annexed table {. extending most which were tenderest,” Vegetable Staticks, Exp. exxiii. t From Sachs, Textbook of Botany, 1882, p. 820.

The several values in this table le very nearly (as we see by Fig. 20) in a smooth curve; in other words a definite law, or principle of continuity, connects the rates of growth at successive points along the growing axis of the root. Moreover this curve, -n its general features, is singularly like those acceleration-curves which we have already studied, in which we plotted the rate of growth against successive intervals of time, as here we have plotted it against successive spatial intervals of an actual growing