12 Gibson, Bodies floating in a Free or a Forced Vortex. 



§ 3. A consideration of the forces acting on a body 

 floating in a free vortex affords an explanation of the 

 seemingly anomalous nature of these results. 



The resultant force is due to : — 



(i) The pressure of the surrounding water. Apart 

 from any relative motion of body and water, this 

 would have a resultant normal to the surface and 

 the body would approach the centre at the same 

 rate as the contiguous filaments. 



(2) The modification introduced by centrifugal action. 

 In a homogeneous body of the same specific 

 gravity as water the centrifugal force being the 

 same as would be exerted on the displaced fluid 

 has no tendency to produce radial motion. If, 

 however, the centre of gravity of the object is 

 below its centre of buoyancy, then on account of 

 the inclined position of the rotating body its 

 effective radius of rotation is greater and this 

 force tends to cause outward motion. If the C.G. 

 is iiigher than the centre of buoyancy the force 

 tends to produce inward motion. 



Thus, due to this cause alone, a light homo- 

 geneous body tends to approach the centre more 

 rapidly than a similar, but heavier body, and the 

 latter more rapidly than a non-homogeneous 

 body of the same shape, size, and weight. This 

 effect will always be more marked the greater the 

 distance between the C.G. and the centre of buoy- 

 ancy, and hence, in a light homogeneous body, 

 the greater the vertical height of the body, so 

 that in such bodies of the same shape and cross- 

 sectional area, the one having the largest vertical 



