196 
Journal of Agricultural Research 
Vol. VII, No. 4 
Integrating equation (1) and transforming to common logarithms, we 
have 
log 10 k = at + c (2) 
in which c is the logarithm of k when t = 0 —that is, at the beginning of 
the period under discussion. Expressing (2) exponentially, we have 
k = 1 o at+c = /e 0 .1 o at (3) 
Therefore if the logarithms of the daily transpiration when plotted 
against the time form a straight line, the condition expressed in equa¬ 
tion (2) is satisfied, and the transpiration, coefficient increases in ac¬ 
cordance with the assumption made above. 
^ The accompanying graphs (fig. 10 to 15) show that an approximate 
linear relationship does exist between the logarithm of the transpira¬ 
tion coefficient and the time in the case of corn, sorghum, Sudan grass, 
Fig. 10.—Graph showing a linear relation between the logarithm of the transpiration-evaporation ratio 
of Sudan grass and the time. 
and alfalfa. The transpiration coefficient of these plants during the 
early stages of growth therefore changes exponentially. 
The numerical value of the coefficient a may now be computed. This 
is represented by the slope of the graphs in figures 10 to 15 and from 
equation (2) it follows that 
_ log k t - log k Q (4) 
The significance of a can be readily seen by a comparison of equation 
(3) with the compound interest law 
= h(i + t> 
\ 100/ ’ 
from which it is evident that 
IO° — I 4 ; 
IOO. 
r 
100 
, or 
a 
