67 
of the maximum of the growth retardation curve in another manner. 
A second phenomenon which shows itself in the combination of 
an omnilateral fore-illumination with a unilateral after-illumination, 
is that which Crark *) calls the increase in sensitiveness of the negative 
reaction. Here also we can find a simple explanation if we suppose 
the existence of a descending portion in the growth retardation curve. 
If the front receives in unilateral illumination an amount of light 
energy just in excess of the maximum, then the back, which 
receives + of this, will still be on the ascending portion. The ordinate 
of the front is still greater than that of the back, hence a positive curva- 
ture occurs. When we now apply more unilateral energy, we shall 
have to shift the points, representing the back and front energy, 
along the growth retardation curve, in such a manner that always 
Ta ta. A negative curvature will then only be possible much 
further on, because of the great distance between zr, and «,, i.e. we, 
will have to pass far beyond the maximum before ya becomes smaller 
than y,; ep need not yet have passed beyond the maximum. When 
then the negative difference of growth retardation y.—y, is great 
enough to become visible in a curvature, a negative curvature will 
occur (about 5000 M.C.S. if administered in 5 mins.). This becomes 
different, however, if «, and #, both lie on the descending portion 
and are less remote from each other; in that case, as soon as w, 
has passed the maximum, the possibility of a negative curvature 
will arise, the front however requires to receive much less than te, 
in order still to render a visible negative curvature possible. By 
means of an artifice we can arrange that vq and 2, come near to 
each other, although both are on the descending portion. This artifice 
consists in giving an omnilateral fore-illumination with a quantity 
of light, which is so great, that front and back both receive a 
quantity of energy corresponding to the maximum of the growth 
retardation curve. If we then unilaterally apply an amount of energy, 
which by itself would have given a strongly positive curvature, 
there will occur a negative curvature, at least if 7a—a, is so large 
that y,—Ya can give a visible effect. Here also the magnitude of the 
difference of growth retardations, and hence the threshold value for the 
negative curvature, will depend on the slope of the growth retardation 
curve, as was the case with the positive curvature. Here some data from 
tables 25 and 26 of Arisz are appended ; I have added the numbers repre- 
senting the quantities of light in M.C.S. which the front and back receive 
from omnilateral fore-illumination + unilateral after-illumination. 
1) QO. L. Crark. Uber negativen Phototropismus bei Avena sativa. Zeitsch. f. 
Botanik. 1913. 
5% 
