Manchester Memoirs, Vol. Hi. {\go?>), No. ^. 9 



When this condition is satisfied, the motion about tiie 

 vertical is simple vibratory of frequency 



/ f a'-h-h } h / V 



per 2tr units of time. 



To illustrate these results experimentally, a uniform 

 rod of length 39"6 cm. was pivoted at one end, and the 

 pivot was moved in an approximately simple vibration of 

 amplitude 3'85 cm. With an applied motion of frequency 

 I r2 per sec, the period of the small oscillations about the 

 vertical was found to be r64 sec. The abo\'e formula, 

 (3), gives r58 sec. The 4% difference may be attributed 

 parti}' to the effect of friction in lengthening the period, 

 and partly to error in the determination of the pivot 

 frequency. 



If the imposed motion is slightly inclined to the 

 vertical, it is observed that the pendulum makes small 

 oscillations about a position much more markedly oblique 

 in the same direction. This effect can be explained very 

 simply. 



Let the inclination of the applied motion be |3, and 

 that of the mean position of the pendulum y. The 

 accelerations due to the applied motion and gravity in 

 this position must be equal and opposite ; i.e., 



-K/r + Zi", 

 and therefore 



/ ajih y, p. gh 



/~'v 1 1 •...2/, I 



t d'/rh J 



1 hus y is large compared with /3 when ;/ is near the limit 

 necessary for stability.* 



Finally, it may be noted that the stability effect still 



* For the determination of the amplitude of the forced oscillation about 

 the mean position, reference may be made to § i of the paper on " Induced 

 Stability '.' already quoted. 



