360 CHAP. XXXII. THE CRITICAL ANGLE 



the sines of the various angles of inclination ; the continuous 

 line represents the excitation at the corresponding angles. 

 It will be noticed that while the divergence between the sines 

 and the reactions is not excessive above 45°, it is very 

 pronounced at the smaller angle of 35° ; it indicates the 

 approach of some hiatus or discontinuity. On producing 

 the curve backwards it intersects the abscissa at or about 

 31-5°, at which angle the excitation would appear to be 

 reduced to zero. This is the critical point ; beyond this 

 angle the excitatory reaction should be abrupt. 



It remains now to ascertain whether such a critical point 

 does actually exist. 



Determination of the Critical Angle 



The discovery of the critical angle was the outcome of 

 my investigations on the geo-electric response of Nymphaea 

 1919). The electric response recorded was that given on 

 inclining the specimen from the vertical to the hori- 

 zontal. This was done very gradually in order to avoid 

 any mechanical disturbance likely to disarrange the electric 

 contacts. There was at first no indication of geotropic exci- 

 tation as the angle was gradually increased from zero, 

 and it was a matter of astonishment to note the reaction 

 which occurred abruptly when the inclination reached the 

 approximate value of 33°. The excitatory reaction was 

 exhibited by the sudden deflection of the hitherto quiescent 

 galvanometer spot of light. On return to the vertical 

 position the excitatory deflection disappeared. Repetition 

 of the experiment gave practically the same result. The 

 only explanation for this unexpected phenomenon is that 

 geotropic excitation is caused by the abrupt fall of heavy 

 particles in the perceptive cells, when the inclination exceeds 

 the critical angle. 



It is necessary at this point to define the critical angle ; 

 it is the angle of inclination at which the excitatory geo- 

 tropic reaction is abruptly manifested. This, as already 



