). from Boas and Wissler’s data.
If we take not merely the variability of stature or weight at a given age, but the variability of the actual successive increments in each yearly period, we see that this latter coefficient of variability tends to increase steadily, and more and more rapidly, within the limits of age for which we have information; and this phenomenon is, in the main, easy of explanation. For a great part of the difference, in regard to rate of growth, between one individual and another is a difference of phase,—a difference in the epochs of acceleration and retardation, and finally in the epoch when growth comes to an end. And it follows that the variability of rate will be more and more marked, as we approach and reach the period when some individuals still continue, and others have already ceased, to grow. In the following epitomised table, {81} I have taken Boas’s determinations of variability (σ) (op. cit. p. 1548), converted them into the corresponding coefficients of variability (σ ⁄ M × 100), and then smoothed the resulting numbers.
| Age | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Boys | 17·3 | 15·8 | 18·6 | 19·1 | 21·0 | 24·7 | 29·0 | 36·2 | 46·1 |
| Girls | 17·1 | 17·8 | 19·2 | 22·7 | 25·9 | 29·3 | 37·0 | 44·8 | — |
The greater variability of annual increment in the girls, as compared with the boys, is very marked, and is easily explained by the more rapid rate at which the girls run through the several phases of the phenomenon.
Just as there is a marked difference in “phase” between the growth-curves of the two sexes, that is to say a difference in the periods when growth is rapid or the reverse, so also, within each sex, will there be room for similar, but individual phase-differences. Thus we may have children of accelerated development, who at a given epoch after birth are both rapidly growing and already “big for their age”; and others of retarded development who are comparatively small and have not reached the period of acceleration which, in greater or less degree, will come to them in turn. In other words, there must under such circumstances be a strong positive “coefficient of correlation” between stature and rate of growth, and also between the rate of growth in one year and the next. But it does not by any means follow that a child who is precociously big will continue to grow rapidly, and become a man or woman of exceptional stature. On the contrary, when in the case of the precocious or “accelerated” children growth has begun to slow down, the backward ones may still be growing rapidly, and so making up (more or less completely) to the others. In other words, the period of high positive correlation between stature and increment will tend to be followed by one of negative correlation. This interesting and important point, due to Boas and Wissler[109], is confirmed by the following table:—
| Age | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
| Stature | (B) | 112·7 | 115·5 | 123·2 | 127·4 | 133·2 | 136·8 | 142·7 | 147·3 | 155·9 | 162·2 |
| (G) | 111·4 | 117·7 | 121·4 | 127·9 | 131·8 | 136·7 | 144·6 | 149·7 | 153·8 | 157·2 | |
| Increment | (B) | 5·7 | 5·3 | 4·9 | 5·1 | 5·0 | 4·7 | 5·9 | 7·5 | 6·2 | 5·2 |
| (G) | 5·9 | 5·5 | 5·5 | 5·9 | 6·2 | 7·2 | 6·5 | 5·4 | 3·3 | 1·7 | |
| Correlation | (B) | ·25 | ·11 | ·08 | ·25 | ·18 | ·18 | ·48 | ·29 | − ·42 | − ·44 |
| (G) | ·44 | ·14 | ·24 | ·47 | ·18 | − ·18 | − ·42 | − ·39 | − ·63 | ·11 |
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.