);) from Quetelet’s Belgian data. The upper curve of stature from Bowditch’s Boston data.
If the child be some 20 inches, or say 50 cm. tall at birth, and the man some six feet high, or say 180 cm., at twenty, we may say that his average rate of growth has been (180 − 50) ⁄ 20 cm., or 6·5 centimetres per annum. But we know very well that this is {62} but a very rough preliminary statement, and that the boy grew quickly during some, and slowly during other, of his twenty years. It becomes necessary therefore to study the phenomenon of growth in successive small portions; to study, that is to say, the successive lengths, or the successive small differences, or increments, of length (or of weight, etc.), attained in successive short increments of time. This we do in the first instance in the usual way, by the “graphic method” of plotting length against time, and so constructing our “curve of growth.” Our curve of growth, whether of weight or length (Fig. [3]), has always a certain characteristic form, or characteristic curvature. This is our immediate proof of the fact that the rate of growth changes as time goes on; for had it not been so, had an equal increment of length been added in each equal interval of time, our “curve” would have appeared as a straight line. Such as it is, it tells us not only that the rate of growth tends to alter, but that it alters in a definite and orderly way; for, subject to various minor interruptions, due to secondary causes, our curves of growth are, on the whole, “smooth” curves.
The curve of growth for length or stature in man indicates a rapid increase at the outset, that is to say during the quick growth of babyhood; a long period of slower, but still rapid and almost steady growth in early boyhood; as a rule a marked quickening soon after the boy is in his teens, when he comes to “the growing age”; and finally a gradual arrest of growth as the boy “comes to his full height,” and reaches manhood.
If we carried the curve further, we should see a very curious thing. We should see that a man’s full stature endures but for a spell; long before fifty[95] it has begun to abate, by sixty it is notably lessened, in extreme old age the old man’s frame is shrunken and it is but a memory that “he once was tall.” We have already seen, and here we see again, that growth may have a “negative value.” The phenomenon of negative growth in old age extends to weight also, and is evidently largely chemical in origin: the organism can no longer add new material to its fabric fast enough to keep pace with the wastage of time. Our curve {63} of growth is in fact a diagram of activity, or “time-energy” diagram[96]. As the organism grows it is absorbing energy beyond its daily needs, and accumulating it at a rate depicted in our
| Stature in metres | Weight in kgm. | Span of arms, male | % ratio of stature to span | |||||
|---|---|---|---|---|---|---|---|---|
| Age | Male | Female | % F ⁄ M | Male | Female | % F ⁄ M | ||
| 0 | 0·500 | 0·494 | 98·8 | 3·2 | 2·9 | 90·7 | 0·496 | 100·8 |
| 1 | 0·698 | 0·690 | 98·8 | 9·4 | 8·8 | 93·6 | 0·695 | 100·4 |
| 2 | 0·791 | 0·781 | 98·7 | 11·3 | 10·7 | 94·7 | 0·789 | 100·3 |
| 3 | 0·864 | 0·854 | 98·8 | 12·4 | 11·8 | 95·2 | 0·863 | 100·1 |
| 4 | 0·927 | 0·915 | 98·7 | 14·2 | 13·0 | 91·5 | 0·927 | 100·0 |
| 5 | 0·987 | 0·974 | 98·7 | 15·8 | 14·4 | 91·1 | 0·988 | 99·9 |
| 6 | 1·046 | 1·031 | 98·5 | 17·2 | 16·0 | 93·0 | 1·048 | 99·8 |
| 7 | 1·104 | 1·087 | 98·4 | 19·1 | 17·5 | 91·6 | 1·107 | 99·7 |
| 8 | 1·162 | 1·142 | 98·2 | 20·8 | 19·1 | 91·8 | 1·166 | 99·6 |
| 9 | 1·218 | 1·196 | 98·2 | 22·6 | 21·4 | 94·7 | 1·224 | 99·5 |
| 10 | 1·273 | 1·249 | 98·1 | 24·5 | 23·5 | 95·9 | 1·281 | 99·4 |
| 11 | 1·325 | 1·301 | 98·2 | 27·1 | 25·6 | 94·5 | 1·335 | 99·2 |
| 12 | 1·375 | 1·352 | 98·3 | 29·8 | 29·8 | 100·0 | 1·388 | 99·1 |
| 13 | 1·423 | 1·400 | 98·4 | 34·4 | 32·9 | 95·6 | 1·438 | 98·9 |
| 14 | 1·469 | 1·446 | 98·4 | 38·8 | 36·7 | 94·6 | 1·489 | 98·7 |
| 15 | 1·513 | 1·488 | 98·3 | 43·6 | 40·4 | 92·7 | 1·538 | 99·4 |
| 16 | 1·554 | 1·521 | 97·8 | 49·7 | 43·6 | 87·7 | 1·584 | 98·1 |
| 17 | 1·594 | 1·546 | 97·0 | 52·8 | 47·3 | 89·6 | 1·630 | 97·9 |
| 18 | 1·630 | 1·563 | 95·9 | 57·8 | 49·0 | 84·8 | 1·670 | 97·6 |
| 19 | 1·655 | 1·570 | 94·9 | 58·0 | 51·6 | 89·0 | 1·705 | 97·1 |
| 20 | 1·669 | 1·574 | 94·3 | 60·1 | 52·3 | 87·0 | 1·728 | 96·6 |
| 25 | 1·682 | 1·578 | 93·8 | 62·9 | 53·3 | 84·7 | 1·731 | 97·2 |
| 30 | 1·686 | 1·580 | 93·7 | 63·7 | 54·3 | 85·3 | 1·766 | 95·5 |
| 40 | 1·686 | 1·580 | 93·7 | 63·7 | 55·2 | 86·7 | 1·766 | 95·5 |
| 50 | 1·686 | 1·580 | 93·7 | 63·5 | 56·2 | 88·4 | — | — |
| 60 | 1·676 | 1·571 | 93·7 | 61·9 | 54·3 | 87·7 | — | — |
| 70 | 1·660 | 1·556 | 93·7 | 59·5 | 51·5 | 86·5 | — | — |
| 80 | 1·636 | 1·534 | 93·8 | 57·8 | 49·4 | 85·5 | — | — |
| 90 | 1·610 | 1·510 | 93·8 | 57·8 | 49·3 | 85·3 | — | — |
curve; but the time comes when it accumulates no longer, and at last it is constrained to draw upon its dwindling store. But in part, the slow decline in stature is an expression of an unequal contest between our bodily powers and the unchanging force of gravity, {64} which draws us down when we would fain rise up[97]. For against gravity we fight all our days, in every movement of our limbs, in every beat of our hearts; it is the indomitable force that defeats us in the end, that lays us on our deathbed, that lowers us to the grave[98].
Side by side with the curve which represents growth in length, or stature, our diagram shows the curve of weight[99]. That this curve is of a very different shape from the former one, is accounted for in the main (though not wholly) by the fact which we have already dealt with, that, whatever be the law of increment in a linear dimension, the law of increase in volume, and therefore in weight, will be that these latter magnitudes tend to vary as the cubes of the linear dimensions. This however does not account for the change of direction, or “point of inflection” which we observe in the curve of weight at about one or two years old, nor for certain other differences between our two curves which the scale of our diagram does not yet make clear. These differences are due to the fact that the form of the child is altering with growth, that other linear dimensions are varying somewhat differently from length or stature, and that consequently the growth in bulk or weight is following a more complicated law.
Our curve of growth, whether for weight or length, is a direct picture of velocity, for it represents, as a connected series, the successive epochs of time at which successive weights or lengths are attained. But, as we have already in part seen, a great part of the interest of our curve lies in the fact that we can see from it, not only that length (or some other magnitude) is changing, but that the rate of change of magnitude, or rate of growth, is itself changing. We have, in short, to study the phenomenon of acceleration: we have begun by studying a velocity, or rate of {65} change of magnitude; we must now study an acceleration, or rate of change of velocity. The rate, or velocity, of growth is measured by the slope of the curve; where the curve is steep, it means that growth is rapid, and when growth ceases the curve appears as a horizontal line. If we can find a means, then, of representing at successive epochs the corresponding slope, or steepness, of the curve, we shall have obtained a picture of the rate of change of velocity, or the acceleration of growth. The measure of the steepness of a curve is given by the tangent to the curve, or we may estimate it by taking for equal intervals of time (strictly speaking, for each infinitesimal interval of time) the actual increment added during that interval of time: and in practice this simply amounts to taking the successive differences between the values of length (or of weight) for the successive ages which we have begun by studying. If we then plot these successive differences against time, we obtain a curve each point upon which represents a velocity, and the whole curve indicates the rate of change of velocity, and we call it an acceleration-curve. It contains, in truth, nothing whatsoever that was not implicit in our former curve; but it makes clear to our eye, and brings within the reach of further investigation, phenomena that were hard to see in the other mode of representation.
The acceleration-curve of height, which we here illustrate, in Fig. [4], is very different in form from the curve of growth which we have just been looking at; and it happens that, in this case, there is a very marked difference between the curve which we obtain from Quetelet’s data of growth in height and that which we may draw from any other series of observations known to me from British, French, American or German writers. It begins (as will be seen from our next table) at a very high level, such as it never afterwards attains; and still stands too high, during the first three or four years of life, to be represented on the scale of the accompanying diagram. From these high velocities it falls away, on the whole, until the age when growth itself ceases, and when the rate of growth, accordingly, has, for some years together, the constant value of nil; but the rate of fall, or rate of change of velocity, is subject to several changes or interruptions. During the first three or four years of life the fall is continuous and rapid, {66} but it is somewhat arrested for a while in childhood, from about five years old to eight. According to Quetelet’s data, there is another slight interruption in the falling rate between the ages of about fourteen and sixteen; but in place of this almost insignificant interruption, the English and other statistics indicate a sudden