MOTION OF VISCOUS FLUIDS 47 



the vortex moves through the surrounding fluid with a resistance almost 

 akin to rolling friction. This accounts for the small resistance experienced. 

 The surrounding water is displaced in a direction at right angles to that 

 of the ring's translation, and thus, with a ring moving horizontally, waves 

 are produced on the surface of the water. 



That the relative motion between the outer layers of the vortex and 

 the surrounding water is very small is shown by the slowness with which 

 the coloured water of the ring diffuses. 



An attempt to propel a solid sphere of approximately the same size and 

 mass as the ring through the fluid by means of a sudden blow, shows 

 very forcibly the relative loss of energy as compared with that of vortex 

 motion. 



The whole subject of the translatory motion of vortices is fraught with 

 difficulty, and no attempt will be made here to discuss this motion 

 analytically. The following may be taken as a partial explanation 

 f the reason of this translation. Consider a vortex ring at the 

 nstant of formation. The velocity at the interior of the aperture is 

 greater than that outside ; the pressure inside is therefore less than that 

 >utside ; and in consequence the ring begins to contract. The effect of 

 his contraction of the aperture is to set up motion in the surrounding 

 luid, which, combined with the cyclic motion inseparable from vortex 

 production, increases the velocities in front of, and decreases those behind 

 he ring. This sets up a difference of pressure at similar points before 

 ind behind the ring, which urges the latter forward with an increasing 

 velocity. A limit to this velocity is reached when the velocity within 

 he aperture approximates to that without. 1 



The mass of fluid forming a vortex has the property that its momentum 

 s unaffected by its angular motion, just as the momentum of a fly-wheel 

 n any direction is unaltered by the fact of the wheel itself rotating about 

 ts own axis, the momentum of the mass in any direction being equal to 

 he mass multiplied by the resolved part of the velocity of its mass centre 

 n that direction. 



When a stream of fluid flows past an immersed solid, at all but the 

 do west velocities eddies are formed in the rear of the solid, which, 

 lowever, are not of the type already described, in that the motion is not 

 low cyclic, the mass comprising an eddy being composed partly of fluid 

 lowing around the edges of the solid and partly of fluid drawn from 

 ts rear face. As a consequence of this there is a continual backward 



1 For an extension of this idea and for an investigation into the motion of vortices, consult 

 [ paper by Mr. W. M. Hicks, " Phil. Trans. Royal Society," 1884, p. J6J, 



