Francis Darwin. 
12 
about an hour. When we begin to study a stimulus, we naturally 
inquire how the reaction is affected by altering the intensity of 
stimulation. Czapek worked with a centrifugal machine, employing 
varying rates of rotation and various radii. There is, however, 
another method of diminishing the stimulus of gravity, namely by 
placing the organ obliquely. If we believe, according to the 
statolith theory, that the gravitational stimulus depends on the 
pressure of heavy particles on the protoplasm of the longitudinal 
cell walls, it is clear that the pressure is nil when the organ is 
vertical, and greatest when it is horizontal, and for intermediate 
oblique positions the pressure will vary with the size of the angle 
which the organ makes with the vertical. Sachs deduced this 
law of the stimulus being proportional to the sine, chiefly from 
theoretic considerations, and Fitting has proved it to be 
approximately true. This, which is generally known as the problem 
of the position of maximum stimulation, has led to a mass of 
contradictory experiment. 
In 1888 Miss Bateson and I 1 made some attempt to solve it. 
Shoots were fixed (by being pinned to boards) in three positions, 
viz., horizontal, 60 n apex upwards, and apex downwards at the same 
angle. They were left so for two hours, when they were released 
and placed in water for an hour. The angles through which they 
curved were then recorded ; the following figures give the averages 
in round numbers :— 
Curvature. 
Or as 
Horizontal 
.. 58° 
• • • 
100 
60° above Hor. 
43 
• • • 
73 
60 n below Hor. 
43 
73 
There was great variability in the individual plants, but the average 
shows a distinct difference in favour of the horizontal position. 
The next experiments were those of Czapek.- He fixed plant- 
organs at various angles to the vertical so that they could not 
curve. After some time they were released and placed in the 
klinostat for twenty-four hours, when the curvatures were measured. 
The general result is that the maximum curvature was produced 
by exposure at 135° from the normal. This means that the 
maximum position for apogeotropism is 45 n below the horizontal, 
and vice versa for pros-geotropic organs. 
In the light of recent work there can be no doubt that neither 
1 Annals of Botany, Vol. II., p. 65. 
2 Pringsheim’s Jahrb., XXVII., 1895, p. 287. 
