222 THE RATE OF GROWTH [ch. 



physiological phenomenon, in that in the former we study (or seek 

 and profess to study) one thing at a time, while in the living body 

 we have constantly to do with factors which interact and interfere; 

 increase in the one case (or change of any kind) tends to be con- 

 tinuous, in the other case it tends to be brought, or to bring 

 itself, 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 

 (Hke growth itself) with the amount or intensity of some external 

 influence, does so under such conditions that progressive increase is 

 followed by progressive decrease; in other words, the function has 

 its optimum condition, and its curve shews a definite maximu^n. 

 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 schadigt oder sie ermiidet ihn, und je hoher sie steigt desto 

 rascher macht sie die Schadigung geltend und desto schneller scbxeitet 

 sie voran*." It is this double effect of temperature on the organism 

 which gives, or helps to give us our "optim'im" curves, which (like 

 all other curves of frequency or error) are the expression, not of a 

 single solitary phenomenon,' but of a more or less complex resultant. 

 Moreover, as Blackman and others have pointed out, our "optimum" 

 temperature is ill-defined until we take account also of the duration 

 of our experiment; for 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. The mile and 

 the hundred yards are won by different runners; and maximum 

 rate of worldng,^ and maximum amount of work done, are two very 

 different things f. 



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 J: 



* On such limiting factors, or counter-reactions, see Putter, Ztschr. f. aUgem. 

 Physiologic, xvi, pp. 574-627, 1914. 



t Cf. L. Errera, UOptimum, 1896 (Recueil d'oeuvres, Physiologie genirale, pp. 338- 

 368, 1910) ; Sachs, Physiologie d. Pflanzen, 1882, p. 233; PfeflFer, Pflanzenphysiologie, 

 n, p. 78, 194; and cf, Jost, Ueber die Reactionsgeschwindigkeit ira Organismus, 

 Biol. CentraWl. xxvi, pp. 225-244, 1906. 



t After Koppen, Bull. Soc. Nat. Moscou, XLin, pp. 41-101, 1871. 



