Jan. 3, 1916 
Hourly Transpiration Rate on Clear Days 
639 
correlated. Reference to figures 12 and 17 shows the unusually close 
agreement between the composite transpiration graph for rye and the 
temperature graph. 
The correlation coefficient of temperature (or wet-bulb depression) 
and transpiration also agrees approximately with that of radiation and 
transpiration. In other words, it appears from a consideration of these 
coefficients that radiation, temperature, and wet-bulb depression show 
an equally close association with the daily transpiration cycle. The 
correlation of temperature and wet-bulb depression with transpiration 
may, however, be l6oked upon as being in part associative with radiation 
rather than causative, as will appear from the following considerations. 
The degree of correlation 1 between radiation and transpiration 
(from 0.82 to 0.88) indicates that the radiation determines the trans¬ 
piration to the extent of from 0.67 to 0.77, the square of the correlation 
coefficients, if radiation is regarded as the primary causative factor. 
The remainder (0.33 to 0.23) is to be ascribed to other factors. If 
temperature is taken as a causative factor of transpiration, the correlation 
coefficients show a dependence of transpiration upon temperature of 
from 0.62 to 0.74; but this is far in excess of the remainder (0.33 to 0.23) 
to be accounted for. In other words, the sum of the squares of the two 
correlation coefficients is in excess of unity. This means, then, that 
temperature and radiation are intercorrelated. A similar intercorrelation 
exists between radiation and wet-bulb depression, and an exact differenti¬ 
ation is impossible. However, since these factors are physically depend¬ 
ent upon radiation, we may assign to radiation the total effect indicated 
by the correlation coefficient, keeping always clearly in mind the assump¬ 
tion involved. On this basis the radiation intensity determines two- 
thirds to three-fourths of the transpiration at Akron on clear days; or 
all other factors combined have only from one-third to one-half the 
influence of radiation. 
On the other hand, if it is preferred to look upon radiation, tempera¬ 
ture, and wet-bulb depression as direct independent causative factors 
(which must also be recognized as involving a specific assumption to 
this effect), then it is evident from Table XXXVII that these factors 
play approximately an equal part in determining transpiration on 
clear days. Not only are the correlation coefficients very nearly the 
same for the different factors with a given crop, but they vary but slightly 
for the different plants investigated. 
1 While a correlation coefficient of unity denotes perfect correlation, a correlation coefficient of less than 
unity must not be interpreted as determining the relationship in proportion to the magnitude of the correla¬ 
tion coefficient, for even in the case of a primary causative factor the relationship can not be greater than the 
square of the correlation coefficient. For example, a correlation coefficient of 0.707 between a causative 
and a resultant term indicates a dependence of the latter upon the former of 0.5—i. e., the square of 0.707. 
This may be easily demonstrated by computing the correlation coefficient between either of two series of 
numbers, each having a normal frequency distribution, with the product of one series by the other. The 
correlation coefficient of the product series with either primary series will be found to be 0.707. In other 
words, each series determines the product series to the extent of 0.5, while the two series together determine 
the product series absolutely. 
