188 
D. T. MACDOUGAL 
with the results of observations upon temperature and growth in the 
two places.^ 
Livingston has recently used a modified summation method 
dealing with temperature effects in phytogeography by which the 
mean normal temperatures are evaluated in terms of a reaction velocity 
assumed to be doubled for every rise of i8° F.,^ and the results cor- 
related with the occurrence of dominant types of vegetation in America. 
Distribution however, is, so far as temperatures are concerned, a 
function of growth or development possibilities and of endurance of 
maxima and minima as has been pointed out by Dr. Shreve. This 
method is then also to be classed as an empirical procedure since the 
rate of growth of a plant through its temperature range is not to be 
expressed in a single formula, and the rate during part of the tonic 
range is much greater than that assumed. Thus the temperature co- 
efficient of growth of Lupinus alhus is 3.7 between 14.4 and 24.2° C, 
4.9 between 17 and 26° C, while that of Zea mais is 5.3 between 24.2 
and 29° C, and 6.4 between 23.5 and 33.5° C. The rate of growth 
of wheat (Triticum vulgar e) between its minimum of 40° F. and 58° F. 
is 5, and the temperature coefficient from 58 to 76° F. is 11, as may 
be seen by reference to figure i . 
The first step in the selection of a standard by which the construc- 
tive processes of organisms might be measured consists in fixing upon 
some form of activity, which is delicately affected by temperature 
and is readily measurable. Growth-extension or expansion seems 
to meet these requirements most fully, and this selection has the 
additional advantage that a large number of measurements of the 
actual rate in several species are already available. 
The graphs representing the rate of growth of the higher plants 
show that these in general begin with a miminum variously placed 
with respect to several species, that the rate runs through several 
degrees of temperature with but little increase, then at a certain 
point the acceleration with the rise in temperature is extremely rapid 
until an optimum is reached. If the temperature rises above this 
point growth and development decrease and rapidly decline to zero. 
^ MacDougal, D. T. The seasonal activities of plants; factors affecting dis- 
tribution and development. Sc. Am. Suppl., October 17, p. 251, 1908. 
^ See Livingston, B. E. Temperature CoefBcient in Plant Geography and Clima- 
tology, Bot. Gaz. 56: 349-375, 1913. The titles of several papers relative to 
reaction velocity in organisms are cited by this author. 
