178 
under the surface *). It is highly questionable, therefore, whether 
their growth will be similarly influenced by the same causes. In 
case these differences are not too great, they may readily be neglected, 
since for making our calenlations it is not necessary, as will be 
seen lower down, to know the reaction of each separate element, 
but only the joint-reaction of the elements in the anterior, and of 
those in the posterior side. If the light in these two halves were 
distributed quite symmetrically, these differences would not avail. In 
the given circumstances they also neutralize each other, however, 
for the greater part, and in this way much of their significance is lost. 
Whether the third hypothesis gives a correct representation of the 
relationship between the sensibility to light and the rate of growth, 
might be ascertained experimentally. To this end one would have 
to compare the sensibility to light and the rate of growth in the 
tip of omnilaterally lighted plants. Such experiments have, however, 
not been made thus far, 
In order to calculate the curvatures on the basis of these hy po- 
theses we have to know how the light is distributed over the two 
halves whose antagonism brings about the curvature, what changes 
the sensibility to light undergoes in those halves, and what is the 
relation between the changes in the rate of growth and those in 
the sensibility to light. ’ 
The distribution of the light over the two antagonistic halves may 
be deduced from the position of either the optimum or the maximum 
of the curve which represents the strength of the curvature as a 
function of the energy. With the optimum the difference in sensibility 
in the two halves must be greatest,”) with the maximum smallest. 
As the difference in sensibility increases so long as the inclination 
of the curve representing the sensibility of the frontal part is steeper 
than that of the curve representing the sensibility of the posterior part, 
it will be greatest when the difference between the inclinations of 
the two curves vanishes, and it will be smallest when the sensibility 
in both parts is lost. In order to determine the changes of the sensi- 
bility in the anterior, and in the posterior side separately we, 
') It is supposed here that the sensibility to light is distributed rather diffusely 
over the whole organ. This is, however, not certain. If it could be demonstrated 
that the sensibility was restricted to a single layer, the elements could be regarded 
as perfectly equal. 
2) This is stated roughly. A given difference in sensibility will, as is shown in 
my paper, bring about a larger curvature according as the average sensibility is 
smaller. In this case, however, the mean sensibilities differ so little that this factor 
does not carry weight. 
