On the possibility of a hydrodynamic model of the electron.
We explore the possibility that the mutual repulsive forces of a uniformly charged sphere could be kept in balance dynamically by a steady circulation of the material, which is assumed to be a nonconducting perfect fluid of uniform density. An exact solution is obtained of Maxwell's equations and of the hydrodynamic equations in the nonrelativistic approximation, which satisfies the boundary conditions on the surface of the sphere. In this solution all the components of the velocity and of the magnetic field are found to vanish on the surface, but not the electric field. The pressure can also be made to vanish on the surface, but in the interior it turns out to be negative, which makes the present solution unacceptable.
Department of Applied Mathematics, The Weizmann Institute, Rehovot, Israel.
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Pekeris