Temper attire on the Rate of Growth in Pisum sativum . 39 
1 and 3. The curve representing the relation of growth to temperature 
cannot, therefore, be regarded as a van ’t Hoff curve. 
Regarding this point, Putter, basing his theory on experiments on 
skin-respiration in the Frog, has attempted to show that the relation between 
temperature and any life-process may be expressed graphically as a van ’t 
Hoff curve, and that deviations from this curve are due to the superposition 
of exponentials. His experiments are however open to objection on the 
ground that he neglects to take into consideration the effect of muscle-tone, 
a point shown by Krogh to be of fundamental importance. Kuijper has 
worked out the relation between temperature and respiration in Lupinus , 
Pisum , and Vicia, and regards the curve which expresses the relation 
as a van ’t Hoff. In this case, however, as in others cited by Putter, only 
the coefficients of the middle region show an approximation to the proper 
magnitude — between 2 and 3 — and this region is arbitrarily chosen as 
that on which most reliance is to be placed. That there is no question 
of a middle region of ‘ correct 5 coefficients giving place, at the two ends, to 
regions in which deviations are due to extreme conditions, is indicated 
by the fact that, in all cases, the coefficients fall continuously from the 
lowest to the highest temperatures. On the other hand, Krogh insists that 
for ‘ standard metabolism ’ in animals, the curve relating temperature to 
intensity is not a van ’t Hoff curve. If we plot my curve with Kuijper’s 
for respiration in Pisum, and Krogh’s for ‘standard metabolism ’, on the 
same axes, we find that the three are strikingly similar (Text-fig. 10) ; and 
this fact strongly supports the view enunciated by Krogh ‘ that the 
temperature relations of physiological processes do follow certain typical 
curves which seem to be identical or nearly related for processes of the same 
fundamental nature in different organisms.’ 
It is interesting, also, to compare Kuijper’s results at high temperatures 
with mine. At 30° and 35 0 he finds a fluctuating rate of respiration, and at 
40° and above, a uniform fall in succeeding time-intervals, also without any 
possibility of extrapolation by Blackman’s method. 
The question of terminology may be referred to here. These growth 
experiments at once suggest the old terminology, minimum, maximum, and 
optimum. But the use of the word ‘ optimum ’ has, since Blackman’s (’05) 
paper on * Optima and Limiting Factors ’, fallen, if not into disuse, at least 
into disrepute. Now the process of growth shows in its relation to tempera- 
ture three well-marked points. — 2 ° C. is the lowest temperature at which 
growth takes place. Between 44 0 and 45 0 lies a point above which growth 
ceases practically instantaneously. About 2 g° lies a point such that any 
increase of temperature means the introduction of a time-factor and the con- 
sequent continuous decrease in the growth-rate. The same three points are 
distinguishable in any of the other processes the relation of which to 
temperature has been studied. The first of these points is the minimum ; 
