64 
In our case we can however follow the course of the growth 
retardation curve more closely by attempting to trace the relation- 
ship between threshold value and fore-illumination. If we calculate 
growth retardation 
sd 
Fig. 2. | energy 
from Artsz’s tables, mentioned above, the ratio of unilateral after- 
illumination to omnilateral fore-illumination, we find that, if after- 
illumination: fore-illumination = 1:11, there is no curvature; 
with this ratio 1:10, 9.9 or 9.2 a few plants give a feeble positive 
curvature, 
with the ratio 1: 7.2 all plants curve positively. 
This applies, as was already said above, only to a fore-illumination 
of less than 2000 M.C.S. given within 3 min. with an intensity 
below 25 M.C. We must, however, recalculate this for the quantities, 
which the anterior and posterior sides receive. Since we see, that 
a feeble positive curvature occurs when the ratio after-illumination : 
fore-illumination (6: a) has reached a definite magnitude 1: 9.7, the 
m—1 
ratio of the energy difference 6—— to the energy of the anterior 
mm 
a 
side — + 6 must also be constant, whatever be the values of m and n. 
n 
In order to demonstrate this numerically, | propose to make certain 
assumptions respecting m and m; in principle it does not matter, 
what values we ascribe to m and 2. For m I assume 4; the back 
is then illuminated with 1*/, of the intensity of the front, receives 
b : 
therefore in unilateral after-illumination E M.C.S. Since the omni- 
lateral energy a M.C.S. is distributed uniformly over the whole 
