304 THE POPULAR SCIENCE MONTHLY 



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 concentra- 

 tion 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 sur- 

 face as the sphere, an almost infmitesimally 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 per- 

 manent 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 E the ethereal viscosity, A the sur- 

 face of discontinuity, and V 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 (F), 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 



F = EAY, 



but with this distinction: The ether has no mass except as it acquires 

 mass by receiving a rotary motion. The dimensional equation for vis- 

 cosity, _ 



, J E = M/LT J 



becomes ' 



L 2 1 i 4 



~T 2 x LT ~ Y 3 



-C/ = -Li X /T72 X 



since the etheral mass is proportional to the energy (which varies as the 

 square of the velocity) impressed upon a volume proportional to r 5 , 

 where r 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, r may be the radius of the ring or of the sur- 

 face. Substituting the value of E in the expression for F, we have 



_ V T2 L U 



