Blackman . — Optima and Limiting Factors. 283 
In later years this factor hardly receives the attention that it deserves. 
Sachs \ however, clearly pointed out that the higher the temperature the 
more quickly the fatal effect ensues, and that short exposure to a very high 
temperature may not kill, when a prolonged exposure to a slightly lower 
temperature is fatal ; see also Pfeffer, Physiology, Section 65. 
Miss Matthaei’s experiments on Carbon-assimilation 2 show, for a given 
case, precisely how important this same time-factor is in the relation of 
a single function to temperatures which are high but not fatal. The facts 
observed indicate the following three laws : — 
(1) At high temperatures (30° C. and above for cherry-laurel) the 
initial rate of assimilation cannot be maintained, but falls off regularly. 
(2) The higher the temperature the more rapid is the rate of 
falling off. 
(3) The falling off at any -given temperature is fastest at first and 
subsequently becomes less rapid. 
This falling off makes it experimentally impracticable to attain the 
highest possible assimilation value at any given temperature. The 
theoretical initial value can, however, be arrived a!t indirectly by continuing 
back the curve of falling values actually attained, taking of course due 
account of the time that elapsed between the initial heating and the earliest 
actual estimation. Besides this first method there is also a second method 
available for arriving at these initial theoretical values, which is based on 
the law of uniform acceleration of reaction mentioned above. At low 
temperatures, below 25 0 C., the assimilation-rate does not fall off appreciably 
with successive estimations — no time-function is involved — therefore at 
these temperatures the first actual estimations made give an exact measure 
of the initial values of the function, and by the relation between them we 
determine the coefficient of increase of rate for a rise of io° C. In the case 
of the cherry-laurel leaf this coefficient is 3 *i. We can then obtain the 
theoretical values for higher temperatures by calculation. 
We have now to apply these two methods to the case of assimilation, 
as to which function alone we have adequate numerical data, and to see 
how far they indicate similar theoretical initial values. 
This is carried out graphically in Diagram I. By the van’t Hoff rule, 
starting from the ascertained values of the assimilation at 9 0 C., and at 
19 0 C., which were 3-8 mg. C 0 2 (A), and 8-o mg. C 0 2 (B) respectively, giving 
the coefficient of 2 -t, we continue the series, and by interpolation on the 
calculated curve obtain the initial value for any desired temperature. The 
values for 30.5 °C. (C), 37 * 5 ° C. (A), 40-5° C. (A), 45 ° C. (A), 50° C. (G), are 
represented by dots in the interrupted line which forms the calculated 
hypothetical curve of the initial relation of assimilation to temperature. 
1 Handbuch der Experimental -Physiologie, 1865, p. 52 ff. 
2 Phil. Trans. Roy. Soc., vol. 197 B, p. 85, 1904. 
X 
