XVII. The complete system of the periods of a hollow vortex ring

Abstract

According to the vortex theory of matter, atoms consist of vortex rings in an infinite perfect liquid, the æther. These rings may be either hollow or filled with otating liquid. The cross section of the hollow or rotating core is in the simplest ase small and the ring is circular. Such vortices have been investigated. It has been hown that they can exist, and that they are stable for certain types of deformation, in this paper the stability of the hollow vortex ring is investigated further, with a view to proving that it is stable for all small deformations of its surface. An attempt also made to make the vortex theory of matter agree with the kinetic theory of ases as regards the relation between the velocity and the energy of an atom. On he latter theory the energy of an atom varies as the square of its velocity, while on he former theory the energy decreases as the velocity increases. As the two theories liffer on a fundamental point, while the consequences of the kinetic theory agree over wide range with experiment, those of the vortex theory are likely to be in discrepancy therewith. However, no account has been taken of the electric change which an atom must hold if electrolysis is to be explained. This electrification will evidently alter the relation between the energy and the velocity. The nature of the change thus produced is here discussed for the case of a hollow vortex, the surface of which behaves as a conductor of electricity, a representation which is dynamically realised by the theory of a rotationally-elastic fluid æther developed in Mr. Larmor’s paper, “A Dynamical Theory of the Electric and Luminiferous Medium.” The small oscillations also are worked out with a view to the discussion of the stability of an electrified vortex. 2. The velocity of translation of the vortex in its steady motion is constant and perpendicular to its plane. By impressing on the whole liquid a velocity equal and opposite to this, the hollow is reduced to rest. Since the cross section of the hollow is small, any small length of it may be regarded as cylindrical. A cylindrical vortex must, by reason of symmetry, have its cross section a circle, so that the cross section of the hollow of the annular vortex is approximately circular, and the hollow itself approximately a tore.