Sir William Thomson on Vortex Atoms. 21 



rapid motion, circulating round the circular axis of the ring with 

 increasing velocity on the circuits nearer and nearer to the ring 

 itself. The circumstances of the actual motion may be imagined 

 thus : — Let a solid column of india-rubber, of circular section, 

 with a diameter small in proportion to its length, be bent into a 

 circle, and its two ends properly spliced together so that it may 

 keep the circular shape when left to itself; let the aperture of 

 the ring be closed by an infinitely thin film ; let an impulsive 

 pressure be applied all over this film, of intensity so distributed 

 as to produce the definite motion of the fluid, specified as follows, 

 and instantly thereafter let the film be all liquefied. This mo- 

 tion is, in accordance with one of Helmholtz's laws, to be along 

 those curves which would be the lines of force, if, in place of the 

 india-rubber circle, were substituted a ring electromagnet*; and 

 the velocities at different points are to be in proportion to the 

 intensities of the magnetic forces in the corresponding points of 

 the magnetic field. The motion, as has long been known, will 

 fulfil this definition, and will continue fulfilling it if the initiating 

 velocities at every point of the film perpendicular to its own plane 

 be in proportion to the intensities of the magnetic force in the 

 corresponding points of the magnetic field. Let now the ring be 

 moved perpendicular to its own plane in the direction with the 

 motion of the fluid through the middle of the ring, with a velo- 

 city very small in comparison with that of the fluid at the centre 

 of the ring. A large approximately globular portion of the fluid 

 will be carried forward with the ring. Let the velocity of the 

 ring be increased ; the volume of fluid carried forward will be 

 diminished in every diameter, but most in the axial or fore-and- 

 aft diameter, and its shape will thus become sensibly oblate. By 

 increasing the velocity of the ring forward more and more, this 

 oblateness will increase, until, instead of being wholly convex, it 

 will be concave before and behind, round the two ends of the axis. 

 If the forward velocity of the ring be increased until it is just 

 equal to the velocity of the fluid through the centre of the ring, 

 the axial section of the outline of the portion of fluid carried for- 

 ward will become a lemniscate. If the ring be carried still faster 

 forward, the portion of it carried with the india-rubber ring will 

 be itself annular ; and, relatively to the ring, the motion of the 

 fluid will be backwards through the centre. In all cases the 

 figure of the portion of fluid carried forward and the lines of 

 motion will be symmetrical, both relatively to the axis and re- 

 latively to the two sides of the equatorial plane. Any one of 

 the states of motion thus described might of course be produced 

 either in the order described, or by first giving a velocity to the 



* That is to say, a circular conductor with a current of electricity main- 

 tained circulating through it. 



