282 
Blackman . — Optima and Limiting Factors. 
I. 
We will at present confine our attention to the condition of temperature, 
and will begin with certain a priori considerations derived from chemical 
dynamics. 
The rate at which all normal chemical change takes place is increased 
by a heightened temperature condition. 
.Most reactions in vitro take place so quickly that it is impossible to 
measure their rate, but with all that go slowly in aqueous solution and 
resemble the processes of the organism, such as the saponification of esters, 
the inversion of sugar by acids, and others, it has been found that the 
acceleration produced by increased temperature is about the same. This 
has been generalized by van’t Hoff 1 into the rule that for every rise of 
io°C. the rate of reaction is about doubled or trebled. 
If this rule of chemical dynamics does not hold good for chemical 
reactions within the organism it is the duty of the physiologist to attempt, 
at any rate, to explain the aberration. Now it is interesting to note that 
this relation has actually been found to hold, as regards medium tempera- 
tures, say from io° C. to 2 f C., for quite a number of cases in animal 
and vegetable organisms so diverse in nature that the law clearly is 
primarily applicable to chemical change in the cell as well as the test-tube. 
Thus the respiration numbers of Clausen 2 , for lupine seedlings and for 
Syringa flowers, show between o° and 20° C., an increase of two and a half 
times for a rise of io° C., the assimilation numbers obtained by Miss Matthaei 
and the writer for cherry-laurel leaves a coefficient of 2-i, and for sun- 
flower leaves 2*3, while to come to more complex metabolic changes, the 
times required for spore-formation in Saccharomyces pastorianus (Herzog 3 ), 
and for the development of frogs’ eggs (as calculated by Cohen from Hertwig’s 
data, cf. Hober 4 ), at different medium temperatures both proceed within the* 
limits of this rule. 
As regards the rate of metabolic chemical change in the organism at 
high temperatures, this law clearly does not express the whole truth. If it 
did we should expect, with increasing temperature, all vital processes to 
proceed with ever-increasing velocity till the fatal temperature was reached 
at which some essential proteid coagulated or some other connexion was 
dislocated, and the whole metabolic machinery came suddenly to a stand- 
still. 
What then does happen as we approach the upper temperature-limit 
of the working of the organism ? An important new factor, the time-factor , 
comes into play. 
1 Vorlesungen ii. theoietiscke Chemie, 189S, Pt. i, English translation, p. 227. 
2 Landvvirtschaftliche Jahrbiicher, 1890, Bd. 19, p. 893. 
3 Zeitschrift f. physiologische Chemie, 1903, Bd. 37, p. 396. 
4 Physikalische Chemie der Zelle u. der Gewebe. Leipzig, 1902. 
