Van’t Hoff’s law, which has become a fundamental principle of chemical mechanics, is likewise applicable (with certain qualifications) to the phenomena of vital chemistry; and it follows that, on very much the same lines, we may speak of the “temperature coefficient” of growth. At the same time we must remember that there is a very important difference (though we can scarcely call it a _fundamental_ one) between the purely physical and the physiological phenomenon, in that in the former we study (or seek and profess to study) one thing at a time, while in the latter we have always to do with various factors which intersect and interfere; increase in the one case (or change of any kind) tends to be continuous, in the other case it tends to be brought to arrest. This is the simple meaning of that _Law of Optimum_, laid down by Errera and by Sachs as a general principle of physiology: namely that _every_ physiological process which varies (like growth itself) with the amount or intensity of some external influence, does so according to a law in which progressive increase is followed by progressive decrease; in other words the function has its _optimum_ condition, and its curve shews a definite _maximum_. In the case of temperature, as Jost puts it, it has on the one hand its accelerating effect which tends to follow van’t Hoff’s law. But it has also another and a cumulative effect upon the organism: “Sie schädigt oder sie ermüdet ihn, und je höher sie steigt, desto rascher macht sie die Schädigung 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 things[140]. ―――――――――― In the case of maize, a certain series of experiments shewed that the growth in length of the roots varied with the temperature as follows[141]: Temperature Growth in 48 hours °C. mm. 18·0 1·1 23·5 10·8 26·6 29·6 28·5 26·5 30·2 64·6 33·5 69·5 36·5 20·7 Let us write our formula in the form _V__{(_t_+_n_)}/_V__{_t_} = _x_^{_n_}. Then choosing two values out of the above experimental series (say the second and the second-last), we have _t_ = 23·5, _n_ = 10, and _V_, _V′_ = 10·8 and 69·5 respectively. Accordingly 69·5/10·8 = 6·4 = _x_^{10}.