1913] LIVINGSTON—TEM PERATURE COEFFICIENTS 365 
for the period and then a quantity equal to 39 times the number of 
days in the average frostless season was substracted from the sum. 
For the summations of temperature efficiencies, the normal 
daily efficiencies corresponding, respectively, to the normal daily 
means of BIGELOW’s tables have simply been added for the same 
days as in the direct summations, thus giving what may be termed 
a tentative index of temperature efficiency for growth during the 
normal frostless season. We shall term this the efficiency index 
and the direct summation will be called the direct index. It is 
these two indices and the charts formed from theni that are to be 
compared. 
To obtain the daily temperature efficiencies corresponding to the 
various normal daily temperature means as the latter are given by 
BIGELOW, it is necessary merely to deduce them from our basic 
assumption, namely, that the growth rate is unity at 4o° F., and 
that it doubles for each rise of 10° C. (18° F.) above this. We shall 
employ the Fahrenheit scale, not because it is in any way as 
Satisfactory as the Centigrade, but because temperature observa- 
tions in the United States and the published data deduced there- 
from have the antiquated form. 
If ¢ be taken as the normal daily mean temperature on the 
Fahrenheit scale, and if u be the corresponding temperature effi- 
ciency for growth, according to our assumption, then 
t—40 
u=218 . 
It is clear that this equation fulfils the assumed conditions, that 
the efficiency doubles with each rise of 18° F., for, if t is 40° F., then 
uisunity; if tis 58° F., then wis 2; if tis 76° F., then u is 4; and so 
on. It becomes necessary, therefore, merely to interpolate between 
the already known values the various values of u corresponding to 
the actual values of ¢ which are to be dealt with. The equation 
just given may as well be written 
log u= 8? (t—40) , 
from which the requisite values of u may readily be obtained. 
Another way of stating the above relation is this: The tempera~ 
