Centrifugal Force as Geo tropic Stimuli. 7 23 
If from P (Fig. 1 ), any point on OL , PR is drawn at right angles to OK , 
, t OR 
then t' ~ OP 
This result may also be expressed in another way. The gravitational 
stimulus acting at right angles to the hypocotyl in the position K is mg , 
but in the position L it is mg cos 0. So that if S' stands for the stimu- 
lating force at right angles to the position K and S' , that at right angles to 
the position L, we have 
S' 
5 = cosd 
t_F 
•• ?~S 
Thus, for the two bending tendencies to neutralize each other, the times 
must be inversely proportional to the stimulating forces which act at right 
angles to the member in the two positions. The result may also be 
expressed as follows : 
St = SO', 
i. e. the product of the stimulating force and its time of action is the same 
in each direction. 
Now it seemed desirable to apply this principle to the case of centri- 
fugal forces. This could be done if we could alternate the stimulus of 
gravity mg acting for a time t in one direction with a centrifugal force 
C acting for a time t' in the opposite direction, each acting at right 
angles to the plant- member in question. Should we find that when the 
times were so arranged that the member in question did not bend in either 
direction, then mgt = Ct'? This is the question which the present research 
sets out to answer. 
Note on the Use of the Term ‘ Centrifugal Force \ 
This term has come into general usage in botanical literature to express 
the geotropic stimulus obtained on a centrifugal wheel, but as the expression 
is of doubtful accuracy, we may with advantage carefully consider to what 
extent the geotropic conditions of stimulus on a centrifugal wheel resemble 
those under the stimulus of gravity acting on a horizontal plant-member. 
The stimulus of gravity may be regarded as follows. If a radicle were 
free to fall indefinitely without any retarding or accelerating force besides 
gravity, no geotropic stimulus would act upon it. Just as a man in a lift 
which, by some accident, fell without restraint, would not be at all conscious 
of gravity until he reached the limit of the fall, so a plant under similar 
circumstances would not perceive any gravitational stimulus. The geotropic 
this a, then a = 90 
been called the ‘ sine law ’. 
9, therefore cos 0 = sin a and the equation may be written 
sin a. This has 
