DETERMINATION OF THE ANGLE 



361 



explained, can be reasonably attributed to the sudden fall of 

 heavy particles on to the sensitive protoplasm of perceptive 

 cells. Displacement of the particles will no doubt occur 

 even at a smaller angle of inclination, but only after a 

 considerable length of time, the displacement being helped 

 by protoplasmic movement ; whereas at the critical angle 

 the excitatory reaction will be immediate. It is very re- 

 markable that the critical angle in the case of Nymphaea 

 should be so near the theo- 

 retical value of 31-5°. The 

 critical angle of 33° found 

 for Nymphaea was a rough 

 approximation. The follow- 

 ing experiments w'ere carried 

 out for the determination of 

 the critical angle in various 

 plants, every precaution being 

 taken for ensuring the highest 

 accuracy. 



Experiment 192. Deter- 

 mination of the critical angle for 

 the petiole of Tropaeolum. — I 

 give a photographic record of 

 the electric response of the 

 petiole of Tropaeolum as its 

 inclination was gradually in- 

 creased from 25° to 31°, by successive steps of 2°. There was 

 no response at 25°, 27°, and 29°. When the inclination 

 reached 31°, response occurred abruptly (fig. 210). Restora- 

 tion of the organ to the vertical w^as attended by recovery. 

 The possible error in the exact setting of the index at 

 zero of the scale is ehminated by observing the effects of 

 alternate inchnations to the right and to the left. The mean 

 of the two effective angles of inchnation thus gives the true 

 value of the critical angle. 



Experiment 193. Exact determination of the critical 

 angle for the petiole of Tropaeolum.— Ih^ angle of inchnation 



Fig. 210. Abrupt geo-electric 

 response at an inclination of 31" 

 (Tropaeolum). 



