of a materialized etheric energy. The enormous density found for the electron is an average density and must be still more exceeded if the mass-giving energy is not distributed uniformly within the volume. By all electric analogies it is natural to assume a superficial concentration of energy in the electron itself. The large apparent density of the electron is perhaps explicable on the assumption that the mass-giving substance is condensed in a very thin surface-layer where it revolves with a velocity smaller than that of light by only a very minute amount. The substance of such a shell should have an almost infinite density. The average density of the enclosed volume should still be very great. If, for example, the electron is a vortex-ring of ether of the same surface as the sphere, an almost infinitesimally thin shell of ether revolving ever so little slower than the velocity of light, is no longer free ether, but becomes matter of almost infinite density, the velocity-gradient falling off very rapidly in the interior of the vortex, and the internal density being negligible. Such a body should possess surface potential, polarity, strong elastic resistance, and other properties demanded of the electron.
If it be admitted that a definite volume of ether can receive a permanent limit, it seems necessary that some surface of discontinuity, as well as a stress, akin to fluid viscosity, exerted between the volume and its surface, should be set up. Calling the ethereal viscosity, the surface of discontinuity, and a velocity, such as the mean velocity in the volume, or the limiting velocity at the surface, to be determined by the nature of the viscous mechanism which is at present unknown, the viscous stress , so far as it depends on dynamic considerations, is equal to a momentum transferred through a definite volume of fluid to a limiting surface at a given speed, and may be represented as in fluid viscosity by the equation
but with this distinction: The ether has no mass except as it acquires mass by receiving a rotary motion. The dimensional equation for viscosity,
becomes
since the etheral mass is proportional to the energy (which varies as the square of the velocity) impressed upon a volume proportional to where is the mean radius of the gyrating volume. In the case of a ring rotating in its own plane, or of a surface rotating around an axis which is a closed curve, may be the radius of the ring or of the surface. Substituting the value of in the expression for , we have
