168 Prof. Dufneld and Mr. Little wood on Correction of a 



(3) The effect which we have considered will always cause 

 a rise of the mercury relative to the barometer tube ; on the 

 other hand, the centrifugal force acting upon the mercury in 

 the tube due to the oscillation about the point of support 

 tends to cause the level to fall. We proceed to consider the 

 amount of this depression before dealing with the conditions 

 which will establish a balance between these two disturbing 

 influences. 



Again take I as the length of the simple equivalent 

 pendulum, a as the deflexion of the pendulum from the 

 vertical at time t. Since the angular velocity O is given 

 dot 



by 



dt 



r e have by differentiating (1) 



12/ cos a, = a cos 6 



dO 

 dt' 



But 



dO 2<rr fq 



where T is the period of the barometer. Thus 



2ira cos 6 



n = 



(2) 



(3) 



17 cos ol 



But the acceleration of the mercury in the tube due to 

 this motion is proportional to O 2 . Consequently 

 we require the average value of that quantity 

 over the period of a swing. 



The average value of II 3 



Fig. 1. 



2 4< 



a 2 f *V2 

 I 2 Jo 



cos- 



r T 2 < cos" a 



which may be shown to be equal to 



47T 2 



ie = a 2 , 



v 



(1 — cosa ). 



If d is the distance of the centre of pressure of the mercury 

 column in the barometer tube below the point of support, 

 the acceleration of the mercury down the tube =£l 2 d. 



If the undisturbed length of the column is h, we have the 

 depression in level Sh given by 



wheuce 



4tt 2 hd , H % lid 



Sh = 



T 2 





_ a 2 d 



9 



(1- 



COS a ) : 



r( 



1 — cos a ). 



