1 8 Gibson, Bodies floatitig in a Free or a Forced Vortex. 



If the positions of the centre of gravity and of the 

 centre of buoyancy do not coincide, centrifugal action, as 

 in the free vortex, tends to produce radial motion, which 

 is inward or outward according as the centre of gravity is 

 above or below the centre of buoyancy, while the same 

 general considerations as regards the effect of different 

 specific gravities, vertical dimensions, and depths of im- 

 mersion, hold true as in the free vortex. The magnitude 

 of the effective centrifugal force is still given by 



^ ,bs. 



pl'^^'^} 



but as V is proportional to r this force is independent of 

 the radius of rotation except in so far as the inclination of 

 the vertical axis of the body varies with the radius. In 

 the forced vortex the inclination increases with the radius 

 so that this force now diminishes as the body approaches 

 the centre and vice versa. 



As in the free vertex, the magnitude of the force at 

 any radius varies as the square of the intensity of the 

 vortex motion. 



In the forced vortex, since the velocity increases as 

 the radius there is no relative tangential velocity, and so 

 no relative rotation of water and solid. 



Where, however, any retardation of the containing 

 vessel takes place, or where a vortex is produced by 

 stirring in a stationary vessel, there is, due to the retarda- 

 tion of the outer filaments by friction, a tendency to 

 inward radial flow along the bottom, accompanied by an 

 outward radial flow over the surface layers. Also, since 

 the tangential velocity does not now increase pro- 

 portionately to the radius, there is a relative tangential 

 motion of solid and fluid which results in a rotation of the 



