Centrifugal Force as Geotropic Stimuli . 
753 
in the vertical plane. Such an instrument is open to the serious objection 
that the plant-members are not subjected to a constant centrifugal force. 
For at the bottom of each rotation gravity 
works with the centrifugal force (giving 
resultant C + mg ) ; at the top of each ro- 
tation gravity works in opposition to the 
centrifugal force (giving resultant C — mg ) ; 
whilst in intervening positions gravity and 
the centrifugal force work at an angle to 
each other producing a resultant which is 
not directed along a radius of the circle of 
rotation. Thus when C is less than mg , the 
resultant force at the top of a rotation acts 
towards the centre of the wheel. 
Pekelharing (TO, pp. 290, 303) has shown that the presentation time 
for centrifugal forces is the same whether the seedlings be placed on a 
centrifuge with horizontal or vertical axis. But Maillefer has not really 
proved that ‘ pour que l’induction geotropique produite par une force f Y soit 
f 
dgale a l’induction produite par une force f 2 , il faut que le rapport soit 
J 2 
egal au rapport f des temps pendant lesquels les forces agissent ’, because 
his forces f x and f 2 were not constant, but vary with each position in each 
revolution. Also when /j or / 2 is less than mg in his experiments, then 
since f — mg will be negative, the force is really a mixture of positive and 
negative forces. 
In the experiments described in this paper the radicles were subjected 
to alternating forces which always acted at right angles to the radicles and 
in opposite directions to each other. One of the alternating forces was 
always gravity and the other was a centrifugal force between 3 mg. and 
and 21 mg. The results obtained show definitely that if gravity acts for 
time t and the centrifugal force for time T y then the radicles remain straight 
C t 
so long as — = y, or CT = mg.t. Or, expressing this generally, if s and 
/ are two stimulating forces acting at right angles to the radicles for 
alternating periods of t and /, then when equilibrium is maintained s.t = s't' } 
i. e. the amount of stimulus in mg. seconds is the same in each direction 
(cf. Maillefer, ' 09 , and Pekelharing, TO). 1 
Since, in the present chaotic state of the science of geotropism, we do 
1 Pekelharing states the law as follows : — ‘ Das Produkt von wirkender Kraft und Reizzeit ist 
konstant.’ She notes that this ‘ Produktregel ’ has been proved for four cases (1) Fitting: Inter- 
mittent stimulation at different angles of inclination ; (2) Pekelharing: Presentation time at different 
angles ; (3) Maillefer : Intermittent stimulation with different centrifugal forces ; (4) Pekelharing : 
Presentation time with different centrifugal forces. 
