86 



THE ROYAL SOCIETY OF CANADA 



Let / = moment of inertia of balancing cylinder about an axis through 

 its centre of gravity at right angles to the plane of vibration. 



Let /i = moment of inertia of balancing cylinder about an axis at 

 right angles to the plane of vibration passing through the point 

 of contact of the two cylinders. Ji will vary in value as vibration 

 occurs. 



Let = angle of inclination of balancing cylinder to the horizontal. 

 6 is always small. 



Condition of Stability 



When the cylinder moves from the horizontal position to the 

 inclined position the point on the balancing cylinder which was in 

 contact with the fixed cylinder at A moves to Ai. 

 .-. GiC = AiB = arc AB = ad. 



The equilibrium will be stable if the vertical through d lies 

 between A and B. Therefore for stability CE must be greater than 

 CD, i.e., ad cos 6 must be greater than b sin 6. 



