Oct. 2 3> 1916 Daily Transpiration during Normal Growth Period 
209 
A SECOND METHOD OF CORRECTING FOR THE CHANGE IN THE TRANSPIRA¬ 
TION COEFFICIENT IN DETERMINING THE CORRELATION OF TRANSPI¬ 
RATION WITH WEATHER FACTORS 
The effect of the change in the transpiration coefficient can also be 
largely avoided in correlation studies involving transpiration through 
recourse to the transpiration-evaporation ratio. If transpiration and 
evaporation show the same hourly response to weather factors, the 
transpiration-evaporation graph for the season would represent the 
progressive changes in the transpiration coefficient. But since the 
transpiration-evaporation graph always presents irregularities owing to 
experimental errors and to the fact that a one-to-one correspondence 
does not exist between the two quantities, it is necessary to make use of 
a smoothed curve through the observations in applying this reduction. 
The ratios for each day of the ordinate of the smoothed graph to the 
maximum ordinate will give the transpiration coefficient for each day 
in terms of the maximum. 1 If, now, we divide the transpiration 
observed on each day by the corresponding ratio of the ordinates, we 
obtain a series of daily transpiration quantities which are independent 
of the size and degree of maturity of the plant, but which still retain 
all the daily fluctuations due to environment. These corrected transpi¬ 
ration quantities can, therefore, be used directly in studying the cor¬ 
relation of transpiration with any given environmental factor. 
In the case of Kubanka wheat, the smoothed transpiration-evaporation 
ratio was represented by two straight lines meeting in a maximum on 
July 12. The daily transpiration of Kubanka has been corrected on 
this basis for the march in the transpiration coefficient and the corre¬ 
lation with the various physical factors determined. The results of the 
computations are given in Table XXV. For comparison, the corre¬ 
lation coefficients based on the first method (ratios of values on consecu¬ 
tive days) have also been included in Table XXV. It will be seen that 
the coefficients determined by the first method are slightly higher than 
those based on the second method. This is to be expected, since the 
second method assumes a one-to-one correspondence between trans¬ 
piration and evaporation, so that departures from such a relationship 
distort the computed transpiration. The difference in the coefficients 
computed by the two methods is, however, usually less than its probable 
1 The daily ratios of the observed transpiration and evaporation can not be used directly, as the following 
discussion will show: 
Let ~ represent the ratio of the transpiration to evaporation at time i, and D^—=k, represent the 
Et £max 
maximum ratio. 
The daily ratio at time t expressed in terms of the maximum is then 
If, now, we divide the observed transpiration Tt by this ratio in order to free the daily observations 
from the effect of the change in the transpiration coefficient, we obtain as the quotient simply kEt. In 
other words, the observed transpiration is dropped from consideration, and the specific assumption is 
made that transpiration is proportional to evaporation. The use of the smoothed graph avoids this as- 
# sumption so far as the transpiration of any given day is concerned. 
