75 2 
Hiley. — On the Value of Different Degrees of 
of inclination, different temperatures, &c., by taking a dozen or so seedlings 
for each experiment, with the trust that differences between individuals will 
neutralize out when an average is taken. Tables of results can of course be 
made out from these experiments, and graphs drawn, but it shows a trust- 
fulness amounting to credulity when a mathematically- minded investigator 
seriously deduces from such a graph that Reaction time = ■ i ^? - n s l an - t - , where 
V sin a 
a is the angle of inclination to the vertical at which the plant-member is 
placed. 1 
Rut fortunately there is another method of work by which this difficulty 
of the individual differences can be overcome. This is to expose one and 
the same seedling alternately to two opposing stimuli so as to let the effects 
of the opposing stimuli neutralize each other in the plant. The relative 
values of the two stimuli can then be reckoned from the relative times 
during which they have acted. The principle of this method was employed 
by Newcombe (’05), Fitting (’05), Haynes (’05), and later by Maillefer (’09). 
By means of his intermittent clinostat, Fitting showed that a hypocotyl 
exposed to the stimulus of gravity, alternately horizontal for a time t, and 
at an angle 0 to the horizontal for a time f remained straight when = cos 0 . 
Now if the letters ^ + / be made to stand for the gravitational stimulus 
/ 
s 
acting at right angles to the hypocotyl in the two positions, then — = cos 0. 
s t 
Thus — = — , or s.t — s /, when the times are so arranged that the stimuli 
s t 
produce a state of equilibrium in the plant. 
Now though Fitting saw this relationship quite clearly, he did not insist 
on it, in view of the fact that the result might be read in other ways. Thus 
suppose 0 — 45 0 ; on any theory of graviperception the effect of a stimulus 
acting at 45° to the long axis of the hypocotyl must be different from the 
stimulus acting at right angles to it, and the difference between the two 
stimuli is not only quantitative, but also qualitative. 2 
Maillefer (’09) applied the principle of alternation of opposing stimula- 
tions to centrifugal forces, and within rather narrow limits obtained results 
similar to those shown in this paper. 3 He did not deal with centrifugal 
forces higher than 2-071 mg. and he used a centrifugal wheel which rotated 
1 Maillefer (’09). 
2 ‘ Aus der Tatsache, dass die geotropischen Erregungen sich annahernd verhalten wie die Sinus 
der Ablenkungswinkel, darf man nicht den Schluss ziehen, dass nur die auf der Langsachse des 
Sprosses rechtwinklige Komponente fiir die Kriimmung in Betracht kommt. Diese Tatsache diirfte 
vielmehr nur aus den Beziehungen zwischen den Reizznstanden, die in verschiedenen Ablenkungs- 
winkeln geschaffen werden, erklart werden konnen. Manches spricht dafiir, dass diese Reizzustande 
nicht nur quantitativ, sondern auch qualitativ verschieden sind.’— Fitting (’05), p. 395 . 
3 I did not know of Maillefer’s paper till all my results had been obtained. 
