66 
2 Tat 
quotient —£ for the threshold value had not been found constant, 
va 
we should only have been allowed to conclude, that the growth 
retardation curve was a curve with decreasing slope, since the 
threshold value increases with increasing a. In that case also we 
might perhaps have obtained some further information about the 
function. I emphasize here that no fundamental significance should 
be attached to the logarithmic course of this part of the curve between 
300 and 900 M.C.S. Moreover the curve from 0—100 M.C.S. is 
certainly not logarithmic; in a subsequent paper Ì hope to refer to 
this point in detail. 
Arisz regards the omnilateral fore-illamination followed by a uni- 
lateral after-illumination as a combination of unilateral illuminations, 
a short one on the posterior side (fore-illumination) and a longer 
one on the anterior side (fore-illamination + after-illumination). 
Since the later posterior side has also received energy during the 
fore-illumination, a tendency to curve in the opposite direction would 
have to be overcome. “It need cause no surprise, that the excess 
which must be given on one of the sides, to obtain an ipsilateral 
curvature, must be greater in proportion as the tendency to curva- 
ture on the other side is stronger.” Arisz therefore likewise explains 
the rise in the threshold value without assuming a change in the 
sensitiveness. This ‘tendency to curve in the opposite direction” 
however, as has been explained above, also exists in plants which 
have had a purely unilateral illumination, for the curvature depends 
on the difference of growth retardation between front and back. As 
in a combined omnilateral fore-illumination and unilateral after-illu- 
mination the growth retardation on the posterior side i.e. the ‘“‘ten- 
dency to curve in the opposite direction”, becomes relatively greater, 
the difference in growth retardation and accordingly, also the resulting 
curvature, becomes smaller (Fig. II). Arisz regards the phototropic 
induction, and hence also the tendency to curve, as a primary reaction, 
but since according to the theory of Braavw, which I have here 
worked out further, the growth retardation is primary and the tendency 
to curve secondary, it is better not to employ the latter expression, 
but to speak of a greater or smaller growth retardation. The unilateral 
illumination is a special case of the omnilateral and not inversely. 
We see therefore, that it is of great importance to ascertain the 
course of the growth retardation curve. We could not well do this 
from the figures of table 1; moreover the energy numbers had to be 
divided by a coefficient in order to make them comparable with those 
for horizontally incident ligbt. We will now try to ascertain the position 
