It is evident that, if we pleased, we might represent the rate of change of acceleration on yet another curve, by constructing a table of “second differences”; this would bring out certain very interesting phenomena, which here however we must not stay to discuss.
| Increment | Increment | |||||
|---|---|---|---|---|---|---|
| Age | Male | Female | Age | Male | Female | |
| 0–1 | 5·9 | 5·6 | 12–13 | 4·1 | 3·5 | |
| 1–2 | 2·0 | 2·4 | 13–14 | 4·0 | 3·8 | |
| 2–3 | 1·5 | 1·4 | 14–15 | 4·1 | 3·7 | |
| 3–4 | 1·5 | 1·5 | 15–16 | 4·2 | 3·5 | |
| 4–5 | 1·9 | 1·4 | 16–17 | 4·3 | 3·3 | |
| 5–6 | 1·9 | 1·4 | 17–18 | 4·2 | 3·0 | |
| 6–7 | 1·9 | 1·1 | 18–19 | 3·7 | 2·3 | |
| 7–8 | 1·9 | 1·2 | 19–20 | 1·9 | 1·1 | |
| 8–9 | 1·9 | 2·0 | 20–21 | 1·7 | 1·1 | |
| 9–10 | 1·7 | 2·1 | 21–22 | 1·7 | 0·5 | |
| 10–11 | 1·8 | 2·4 | 22–23 | 1·6 | 0·4 | |
| 11–12 | 2·0 | 3·5 | 23–24 | 0·9 | −0·2 | |
| 12–13 | 4·1 | 3·5 | 24–25 | 0·8 | −0·2 | |
* The values given in this table are not in precise accord with those of the Table on p. [63]. The latter represent Quetelet’s results arrived at in 1835; the former are the means of his determinations in 1835–40.
The acceleration-curve for man’s weight (Fig. [5]), whether we draw it from Quetelet’s data, or from the British, American and other statistics of later writers, is on the whole similar to that which we deduce from the statistics of these latter writers in regard to height or stature; that is to say, it is not a curve which continually descends, but it indicates a rate of growth which is subject to important fluctuations at certain epochs of life. We see that it begins at a high level, and falls continuously and rapidly[100] {69} during the first two or three years of life. After a slight recovery, it runs nearly level during boyhood from about five to twelve years old; it then rapidly rises, in the “growing period” of the early teens, and slowly and steadily falls from about the age of sixteen onwards. It does not reach the base-line till the man is about seven or eight and twenty, for normal increase of weight continues during the years when the man is “filling out,” long after growth in height has ceased; but at last, somewhere about thirty, the velocity reaches zero, and even falls below it, for then the man usually begins to lose weight a little. The subsequent slow changes in this acceleration-curve we need not stop to deal with.
Fig. 5. Mean annual increments of weight, in man and woman; from Quetelet’s data.
In the same diagram (Fig. [5]) I have set forth the acceleration-curves in respect of increment of weight for both man and woman, according to Quetelet. That growth in boyhood and growth in girlhood follow a very different course is a matter of common knowledge; but if we simply plot the ordinary curve of growth, or velocity-curve, the difference, on the small scale of our diagrams, {70} is not very apparent. It is admirably brought out, however, in the acceleration-curves. Here we see that, after infancy, say from three years old to eight, the velocity in the girl is steady, just as in the boy, but it stands on a lower level in her case than in his: the little maid at this age is growing slower than the boy. But very soon, and while his acceleration-curve is still represented by a straight line, hers has begun to ascend, and until the girl is about thirteen or fourteen it continues to ascend rapidly. After that age, as after sixteen or seventeen in the boy’s case, it begins to descend. In short, throughout all this period, it is a very similar curve in the two sexes; but it has its notable differences, in amplitude and especially in phase. Last of all, we may notice that while the acceleration-curve falls to a negative value in the male about or even a little before the age of thirty years, this does not happen among women. They continue to grow in weight, though slowly, till very much later in life; until there comes a final period, in both sexes alike, during which weight, and height and strength all alike diminish.
From certain corrected, or “typical” values, given for American children by Boas and Wissler (l.c. p. 42), we obtain the following still clearer comparison of the annual increments of stature in boys and girls: the typical stature at the commencement of the period, i.e. at the age of eleven, being 135·1 cm. and 136·9 cm. for the boys and girls respectively, and the annual increments being as follows:
| Age | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Boys (cm.) | 4·1 | 6·3 | 8·7 | 7·9 | 5·2 | 3·2 | 1·9 | 0·9 | 0·3 |
| Girls (cm.) | 7·5 | 7·0 | 4·6 | 2·1 | 0·9 | 0·4 | 0·1 | 0·0 | 0·0 |
| Difference | −3·4 | −0·7 | 4·1 | 5·8 | 4·3 | 2·8 | 1·8 | 0·9 | 0·3 |
The result of these differences (which are essentially phase-differences) between the two sexes in regard to the velocity of growth and to the rate of change of that velocity, is to cause the ratio between the weights of the two sexes to fluctuate in a somewhat complicated manner. At birth the baby-girl weighs on the average nearly 10 per cent. less than the boy. Till about two years old she tends to gain upon him, but she then loses again until the age of about five; from five she gains for a few years somewhat rapidly, and the girl of ten to twelve is only some 3 per cent. less in weight than the boy. The boy in his teens gains {71} steadily, and the young woman of twenty is nearly 15 per cent. lighter than the man. This ratio of difference again slowly diminishes, and between fifty and sixty stands at about 12 per cent., or not far from the mean for all ages; but once more as old age advances, the difference tends, though very slowly, to increase (Fig. [6]).