Temperature on the Rate of Growth in Pisum sativum . 41 
presence of a time-factor, and a change in the conception of the meaning of 
the optimum has become necessary. It is absurd to apply the term, as 
Kuijper does, to a temperature at which the process shows a very high 
initial intensity and then a more or less rapid drop to an intensity below 
that obtained at lower temperatures. It seems logical, on the other hand, to 
apply it to the highest temperature at which the process takes place at 
a constant rate. What is important is, that this point possesses an objective 
reality just as do the maximum and minimum points. 
If the term ‘optimum 5 is used in this sense, it becomes necessary 
to distinguish another point at which the intensity of the process is at 
its maximum. This may be illustrated by reference to the relation of 
temperature to respiration in Pisum. Kuijper, by using very short 
experimentation-times, finds that the initial intensity of respiration is higher 
with rising temperature almost to the maximum temperature. Probably 
with infinitely short periods it would be found that at the maximum 
temperature the initial intensity would be the maximum intensity for a very 
short time. That is, the maximum-rate temperature would coincide with 
the maximum temperature. In the case of growth, the relation is different. 
The highest measured rate occurs in the first ten minutes at 30-3°, and it has 
been shown that, at higher temperatures, a higher rate does not occur even 
for a very short time. Between 38° and 30° lies the optimum point. Its 
exact determination experimentally is a matter of very great difficulty, if it 
is, in fact, at all possible. But it seems probable that, if exact analysis of 
this interval could be carried out, there would be found a temperature 
at which the rate would be equal to, or higher than, that at 30*3° and 
at which no time-factor would be in operation. This would be the optimum, 
and, in this case, the maximum-rate temperature would ultimately coincide 
with the optimum. The probable coincidence, in the limiting case of the 
maximum-rate temperature, with the optimum or the maximum cannot be 
demonstrated, on the one hand, because of the curvatures which take place, 
and on the other, because it is impossible to experiment with infinitely short 
periods. Therefore the maximum-rate temperature remains, at least experi- 
mentally, distinct. 
It would seem, then, that four cardinal points are to be distinguished 
for all investigated physiological processes : 
The minimum temperature for any process is the lowest temperature at 
which the process takes place. 
The maximum temperature is the highest temperature at which the 
process takes place. 
The optimum temperature is the highest temperature at which there is 
no time-factor operating, and 
The maximum-rate temperature is that temperature at which the pro- 
cess attains to its highest intensity. 
