successive periods, such as years or days, but with these increments represented as percentages of the amount which had been reached at the end of the former period. For instance, taking Queteletãs values for the height in centimetres of a male infant from birth to four years old, as follows:
| Years | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| cm. | 50ôñ0 | 69ôñ8 | 79ôñ1 | 86ôñ4 | 92ôñ7 |
Minot would state the percentage growth in each of the four annual periods at 39ôñ6, 13ôñ3, 9ôñ6 and 7ôñ3 per cent. respectively.
Now when we plot actual length against time, we have a perfectly definite thing. When we differentiate this Lã₤ãã₤T, we have dLã₤ãã₤dT, which is (of course) velocity; and from this, by a second differentiation, we obtain dÿ£¢2ãLã₤ãã₤dTÿ£¢2ã₤, that is to say, the acceleration.
But when you take percentages of y, you are determining dyã₤ãã₤y, and when you plot this against dx, you have
that is to say, you are multiplying the thing you wish to represent by another quantity which is itself continually varying; and the result is that you are dealing with something very much less easily grasped by the mind than the original factors. Professor Minot is, of course, dealing with a perfectly legitimate function of x and y; and his method is practically tantamount to plotting logã₤y against x, that is to say, the logarithm of the increment against the time. This could only be defended and justified if it led to some simple result, for instance if it gave us a straight line, or some other simpler curve than our usual curves of growth. As a matter of fact, it is manifest that it does nothing of the kind.
Pre-natal and post-natal growth.
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