CHAPTER III THE RATE OF GROWTH

and a cumulative effect upon the organism: 〜Sie schûÊdigt oder sie ermû¥det ihn, und je hûÑher sie steigt, desto rascher macht sie die SchûÊdigung geltend und desto schneller schreitet sie voran.〝 It would seem to be this double effect of temperature in the case of the organism which gives us our 〜optimum〝 curves, which are the expression, accordingly, not of a primary phenomenon, but of a more or less complex resultant. Moreover, as Blackman and others have pointed out, our 〜optimum〝 temperature is very ill-defined until we take account also of the duration of our experiment; for obviously, a high temperature may lead to a short, but exhausting, spell of rapid growth, while the slower rate manifested at a lower temperature may be the best in the end. {111} The mile and the hundred yards are won by different runners; and maximum rate of working, and maximum amount of work done, are two very different things⁵⁹.

In the case of maize, a certain series of experiments shewed that the growth in length of the roots varied with the temperature as follows⁶⁰:

Let us write our formula in the form

Then choosing two values out of the above experimental series (say the second and the second-last), we have t =ã€₤23ôñ5, n =ã€₤10, and V, Vÿ£¢ã€ý =ã€₤10ôñ8 and 69ôñ5 respectively.

Accordingly

Therefore

And,

This first approximation might be considerably improved by taking account of all the experimental values, two only of which we have as yet made use of; but even as it is, we see by Fig. 26 that it is in very fair accordance with the actual results of observation, within those particular limits of temperature to which the experiment is confined. {112}

For an experiment on Lupinus albus, quoted by Asa Gray⁶¹, I have worked out the corôÙreôÙsponôÙding coefficient, but a little more carefully. Its value I find to be 1ôñ16, or very nearly identical with that we have just found for the maize; and the corôÙreôÙsponôÙdence between the calculated