Manchester 2Icj}ioirs, Vol. /v. {icjii). No. 1. 13 



dimensions tends to approach the centre most 

 rapidly. 



If [Fibs, be the weight of the body ; r the 

 radius of the path of its C.G. ; f\ that of the 

 path of the centre of buoyancy ; v the velocity 

 of the mass-centre and z\ of the centre of buoy- 

 ancy, then at a given instant 



V1-. 



and the resultant radial outward force acting in 

 virtue of centrifugal action is given by 



g w- f\ ) g { r > 



Since in a free vortex vof , this force 



r 



becomes directly proportional to r — r^, and in- 

 versely proportional to r'^. Owing to the in- 

 creasing inclination of the body as the centre is 

 approached r—i\ increases as r diminishes, so 

 that this effect varies inversely as a higher power 

 of the radius than the fourth. 



If the intensity of the vortex be defined as 

 the velocity at a given radius, this action will 

 evidentl)^ vary as the square of the intensity. 



(3) The fact that, since the velocity of the water varies 

 inversely as the distance from the centre, there is 

 a relative motion of water and solid, in the 

 direction of revolution, over that portion of the 

 periphery marked nba in the Figure, and, in the 

 opposite direction, over the periphery marked aca. 

 This causes the body to rotate about its own axis 

 relatively to the surrounding zvater^ in the opposite 

 direction to that of its revolution around the 



