many cases ãinterpolateã 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 mathôÙeôÙmatôÙiôÙcal expression), to ãextrapolateã 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 Rû¥ssowãs25, 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 | 67ôñ5 | 68 | 69 | 70ôñ5 | 72 |
| [DifôÙferôÙencôÙes (in cm.) | 4 | 4 | 2 | 2 | 2 | 1 | 1 | 1ôñ5 | ôñ5 | 1 | 1ôñ5 | 1ôñ5] |
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