between the hands. Just the same motion of rotation it has on the
stick, only that the ends are now joined together. All the inside
surface of the ring is going one way, namely, the way the stick
is pulled; and all the outside is going the other way. Such a
vortex-ring is made by the smoker who purses his lips into a
round hole and sends out a puff of smoke. The outside of the ring
is kept back by the friction of his lips while the inside is
going forwards; thus a rotation is set up all round the
smoke-ring as it travels out into the air." In these cases, and
in others as we commonly find it, vortex-motion owes its origin
to friction and is after a while brought to an end by friction.
But in 1858 the equations of motion of an incompressible
frictionless fluid were first successfully solved by Helmholtz,
and among other things he proved that, though vortex-motion could
not be originated in such a fluid, yet supposing it once to
exist, it would exist to all eternity and could not be diminished
by any mechanical action whatever. A vortex-ring, for example, in
such a fluid, would forever preserve its own rotation, and would
thus forever retain its peculiar individuality, being, as it
were, marked off from its neighbour vortex-rings. Upon this
mechanical truth Sir William Thomson based his wonderfully
suggestive theory of the constitution of matter. That which is
permanent or indestructible in matter is the ultimate homogeneous
atom; and this is probably all that is permanent, since chemists
now almost unanimously hold that so-called elementary molecules
are not really simple, but owe their sensible differences to the
various groupings of an ultimate atom which is alike for all.
Relatively to our powers of comprehension the atom endures
eternally; that is, it retains forever unalterable its definite
mass and its definite rate of vibration. Now this is just what a