EARTHQUAKE SHOCKS AND OTHER CONCUSSIONS. 223 



F 



The elastic force for unity of displacement at radius k is equal to ^ . 



F 

 For an angular displacement or distance k 6, it is T-#. This tends to redress C. 



The effect of gravity in displacing C is 



MA sin 0, ' 



or Mk6 nearly, when the displacement is not large. 



Hence the pressure on C tending to stability is 



The accelerating force on C is 



g being the accelerating effect of the force of gravity. Hence equilibrium is 



Stable 



h 

 as=r=: = 

 unstaoie 



I 



When the pendulum-rod forms an angle & with the vertical, the displacement 

 s of the ball, which moves with a radius k, is k 6. Hence Q s -, and the redressing 



/C 



force is (by Eq. (a) ) 



And if <p represent the Accelerating Force for unity of displacement of the ball 



II. To determine the motion of the pendulum when a uniform velocity is 

 suddenly communicated to the base. 



x = movement of stand, 



y = movement of ball, 



s = y _ x = relative movement of ball. 



Let the motion of A be uniform for a certain tune t with velo- 

 city V, then x V t, 



X 



A 



ds _dy ( ~ 



dl-JT 



d*s _ d?y ,< 



d P ~ d t* 



Force causing C to follow A (having always an opposite sign from s), = $ s 

 (<j> being the elastic action of the Avire on C for s = 1) as above ; Eq. (6). 

 VOL. xv. PART i. 3 o 



