For an experiment on Lupinus albus, quoted by Asa Gray[142], I have worked out the corresponding coefficient, but a little more carefully. Its value I find to be 1·16, or very nearly identical with that we have just found for the maize; and the correspondence between the calculated curve and the actual observations is now a close one.
Fig. 26. Relation of rate of growth to temperature in Maize. Observed values (after Köppen), and calculated curve.
Since the above paragraphs were written, new data have come to hand. Miss I. Leitch has made careful observations of the rate of growth of rootlets of the Pea; and I have attempted a further analysis of her principal results[143]. In Fig. [27] are shewn the mean rates of growth (based on about a hundred experiments) at some thirty-four different temperatures between 0·8° and 29·3°, each experiment lasting rather less than twenty-four hours. Working out the mean temperature coefficient for a great many combinations of these values, I obtain a value of 1·092 per C.°, or 2·41 for an interval of 10°, and a mean value for the whole series showing a rate of growth of just about 1 mm. per hour at a temperature of 20°. My curve in Fig. [27] is drawn from these determinations; and it will be seen that, while it is by no means exact at the lower temperatures, and will of course fail us altogether at very high {113} temperatures, yet it serves as a very satisfactory guide to the relations between rate and temperature within the ordinary limits of healthy growth. Miss Leitch holds that the curve is not a van’t Hoff curve; and this, in strict accuracy, we need not dispute. But the phenomenon seems to me to be one into which the van’t Hoff ratio enters largely, though doubtless combined with other factors which we cannot at present determine or eliminate.
Fig. [27]. Relation of rate of growth to temperature in rootlets of Pea. (From Miss I. Leitch’s data.)
While the above results conform fairly well to the law of the temperature coefficient, it is evident that the imbibition of water plays so large a part in the process of elongation of the root or stem that the phenomenon is rather a physical than a chemical one: and on this account, as Blackman has remarked, the data commonly given for the rate of growth in plants are apt to be {114} irregular, and sometimes (we might even say) misleading[144]. The fact also, which we have already learned, that the elongation of a shoot tends to proceed by jerks, rather than smoothly, is another indication that the phenomenon is not purely and simply a chemical one. We have abundant illustrations, however, among animals, in which we may study the temperature coefficient under circumstances where, though the phenomenon is always complicated by osmotic factors, true metabolic growth or chemical combination plays a larger role. Thus Mlle. Maltaux and Professor Massart[145] have studied the rate of division in a certain flagellate, Chilomonas paramoecium, and found the process to take 29 minutes at 15° C., 12 at 25°, and only 5 minutes at 35° C. These velocities are in the ratio of 1 : 2·4 : 5·76, which ratio corresponds precisely to a temperature coefficient of 2·4 for each rise of 10°, or about 1·092 for each degree centigrade.
By means of this principle we may throw light on the apparently complicated results of many experiments. For instance, Fig. [28] is an illustration, which has been often copied, of O. Hertwig’s work on the effect of temperature on the rate of development of the tadpole[146].
From inspection of this diagram, we see that the time taken to attain certain stages of development (denoted by the numbers III–VII) was as follows, at 20° and at 10° C., respectively.
| At 20° | At 10° | |||
|---|---|---|---|---|
| Stage | III | 2·0 | 6·5 | days |
| ″ | IV | 2·7 | 8·1 | ″ |
| ″ | V | 3·0 | 10·7 | ″ |
| ″ | VI | 4·0 | 13·5 | ″ |
| ″ | VII | 5·0 | 16·8 | ″ |
| Total | 16·7 | 55·6 | ″ |