326 TEXTBOOK OF PLANT PHYSIOLOGY 



stimulation, which appears to be in proportion to the sine of the 

 angle of deviation. This is known as the law of the sine. There- 

 fore, the time of presentation seems to be least in a horizontal 

 position and increases with the gradual approach to the vertical 

 line. The product obtained by multiplying the time of presenta- 

 tion by the sine of the angle of deviation is a constant quantity. 



By changing the angle of deviation, it is possible only to 

 decrease the strength of the geotropic stimulus. In order to 

 increase it, it is necessary to apply the effect of a different force, 

 which also produces an acceleration of mass, namely, centrifugal 

 force. If the shoots of plants are fixed in a vertical position on 

 the circumference of a horizontally placed wheel which is rotated 

 at considerable speed, it will be found that during further growth, 

 the seedlings will deviate 'from their vertical position. Their stems 

 will be directed towards the center, and the roots away from it. 

 By altering the speed of rotation it is possible to change the angle 

 of deviation from the vertical line. By this means it has been 

 found that the direction of the axial organs will always correspond 

 to the resultant between the force of gravity and centrifugal force. 

 In case of very rapid rotation, when the centrifugal force is 

 greater than that of gravitation, the shoots will grow almost 

 horizontally. And when the speed of rotation is such that the 

 centrifugal force is equal to the force of gravity, then the shoots 

 will grow at an angle of 45 deg. 



By subjecting the shoots to the effect of centrifugal force during 

 a short period and then transferring them to the klinostat, it is 

 possible to obtain the same curvatures as are secured after a short 

 exposure to the effect of gravity. It is also possible to determine 

 a definite time of presentation for each intensity of centrifugal 

 force. This time has been found to be in inverse proportion to 

 the magnitude of the force used. In this case also one secures a 

 full confirmation of the law of the quantity of stimulus which has 

 been considered already in studying phototropism. 



Geotropic stimuli are not equally perceived by all parts of 

 an organ possessing geotropic sensitivity. As with phototropic 

 stimuli, so here, the tip of the curving organ has been found to be 

 the most sensitive part. The distribution of geotropic sensitivity 

 may be most conveniently studied in the root. Charles Darwin 

 (1880) showed that the tip of the root, or the last 1 to 2 mm., is 

 the seat of sensitivity, and that roots with tips cut off grow hori- 



