Читать книгу On Growth and Form - D'Arcy Wentworth Thompson - Страница 10

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In the acceleration-curves which we have shown above (Figs. 2, 3), it will be seen that the curve starts at a considerable interval from the actual date of birth; for the first two increments which we can as yet compare with one another are those attained during the first and second complete years of life. Now we can in many cases “interpolate” with safety between known points upon a curve, but it is very much less safe, and is not very often justifiable (at least until we understand the physical principle involved, and its math­e­mat­i­cal expression), to “extrapolate” beyond the limits of our observations. In short, we do not yet know whether our curve continued to ascend as we go backwards to the date of birth, or whether it may not have changed its direction, and descended, perhaps, to zero-value. In regard to length, or stature, however, we can obtain the requisite information from certain tables of Rüssow’s103, who gives the stature of the infant month by month during the first year of its life, as follows:

Age in months	0	1	2	3	4	5	6	7	8	9	10	11	12
Length in cm.	(50)	54	58	60	62	64	65	66	67·5	68	69	70·5	72
[Dif­fer­enc­es (in cm.)	4	4	2	2	2	1	1	1·5	·5	1	1·5	1·5]

If we multiply these monthly differences, or mean monthly velocities, by 12, to bring them into a form comparable with the {74} annual velocities already represented on our acceleration-curves, we shall see that the one series of observations joins on very well with the other; and in short we see at once that our acceleration-curve rises steadily and rapidly as we pass back towards the date of birth.

Fig. 7. Curve of growth (in length or stature) of child, before and after birth. (From His and Rüssow’s data.)

But birth itself, in the case of a viviparous animal, is but an unimportant epoch in the history of growth. It is an epoch whose relative date varies according to the particular animal: the foal and the lamb are born relatively later, that is to say when development has advanced much farther, than in the case of man; the kitten and the puppy are born earlier and therefore more helpless than we are; and the mouse comes into the world still earlier and more inchoate, so much so that even the little marsupial is scarcely more unformed and embryonic. In all these cases alike, we must, in order to study the curve of growth in its entirety, take full account of prenatal or intra-uterine growth. {75}

According to His104, the following are the mean lengths of the unborn human embryo, from month to month.

Months	0	1	2	3	4	5	6	7	8	9	10 (Birth)
Length in mm.	0	7·5	40	84	162	275	352	402	443	472	490–500
Increment per month in mm.	—	7·5	32·5	44	78	113	77	50	41	29	18–28

Fig. 8. Mean monthly increments of length or stature of child (in cms.).

These data link on very well to those of Rüssow, which we have just considered, and (though His’s measurements for the pre-natal months are more detailed than are those of Rüssow for the first year of post-natal life) we may draw a continuous curve of growth (Fig. 7) and curve of acceleration of growth (Fig. 8) for the combined periods. It will at once be seen that there is a “point of inflection” somewhere about the fifth month of intra-uterine life105: up to that date growth proceeds with a continually increasing {76} velocity; but after that date, though growth is still rapid, its velocity tends to fall away. There is a slight break between our two separate sets of statistics at the date of birth, while this is the very epoch regarding which we should particularly like to have precise and continuous information. Undoubtedly there is a certain slight arrest of growth, or diminution of the rate of growth, about the epoch of birth: the sudden change in the {77} method of nutrition has its inevitable effect; but this slight temporary set-back is immediately followed by a secondary, and temporary, acceleration.

Fig. 9. Curve of pre-natal growth (length or stature) of child; and cor­re­spon­ding curve of mean monthly increments (mm.).

It is worth our while to draw a separate curve to illustrate on a larger scale His’s careful data for the ten months of pre-natal life (Fig. 9). We see that this curve of growth is a beautifully regular one, and is nearly symmetrical on either side of that point of inflection of which we have already spoken; it is a curve for which we might well hope to find a simple math­e­mat­i­cal expression. The acceleration-curve shown in Fig. 9 together with the pre-natal curve of growth, is not taken directly from His’s recorded data, but is derived from the tangents drawn to a smoothed curve, cor­re­spon­ding as nearly as possible to the actual curve of growth: the rise to a maximal velocity about the fifth month and the subsequent gradual fall are now demonstrated even more clearly than before. In Fig. 10, which is a curve of growth of the bamboo106, we see (so far as it goes) the same essential features, {78} the slow beginning, the rapid increase of velocity, the point of inflection, and the subsequent slow negative acceleration107.

Fig. 10. Curve of growth of bamboo (from Ostwald, after Kraus).