101 
oj Edinburgh , Session 1866 - 67 . 
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 velocity 
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 in- 
crease, until, instead of being wholly convex it will be concave, 
before and behind, round the two ends of the axis. If the forw r ard 
velocity of the ring be increased until it is just equal to the velo- 
city of the fluid, through the centre of the ring, the axial section 
of the outline of the portion of fluid carried forward 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 relatively 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 ring, and then setting the fluid in motion by aid 
of an instantaneous film, or by applying the two initiative actions 
simultaneously. The whole amount of the impulse required, or, as 
we may call it, the effective momentum of the motion, or simply 
the momentum of the motion, is the sum of the integral values of 
the impulses on the ring and on the film required to produce one 
or other of the two components of the whole motion. Now it is 
obvious that, as the diameter of the ring is very small in compari- 
son with the diameter of the, circular axis, the impulse on the ring 
must be very small in comparison with the impulse on the film, 
unless the velocity given to the ring is much greater than that 
given to the central parts of the film. Hence, unless the velocity 
given to the ring is so very great as to reduce the volume of the 
fluid carried forward with it to something not incomparably greater 
