Manchester Memoirs, Vol. Iv. (191 1), No. 7. 15 



portion of the wake will be deflected outivards by the 

 rotation,* and the corresponding force on the body will, 

 in consequence, have an inward radial component. As, 

 however, the relative velocity is greater over the portions 

 of the body nearer the centre of the vortex, the resultant 

 force will have an o?ifzi'ard rsidial component. The relative 

 magnitude of this is likely to be greater the larger the 

 diameter of the body, and the greater its depth of im- 

 mersion ; and, for bodies of different shapes, is likely to 

 be least where eddy formation in the rear of the body 

 is least marked, and therefore, with bodies of a more or 

 less circular cross section. 



Since the magnitude of these forces will vary approxi- 

 mately as the square of the velocity, it will vary approxi- 

 mately as the inverse square of the radius in a vortex of 

 given intensity, and as the square of the intensity where 

 the latter varies. 



Where the resultant of all the forces hitherto mentioned 

 tends to make a body approach the centre more rapidly 

 than the contiguous filaments of fluid, the resistance to 

 this motion will be greater the larger the under-water 

 area of the body, projected in the direction of motion, and 

 will also be greater the more the body departs from the 

 spherical form. 



Still a further action complicates the behaviour of a 

 floating bod}'. Owing to the friction of the lower layers of 

 water over the bottom of the containing vessel, the velocity 

 of whirl at a given radius is less than at points in the same 

 vertical but nearer the surface. The centrifugal force of 

 the bottom particles thus becomes insufficient to counter- 

 balance the tendency to inward flow caused by the super- 



• These deflections of the wake were shown by means of colour bands 

 of aniline dye, escaping from small holes pierced around the periphery of a 

 hollow cylindrical floating body, containing aniline solution. 



