Let a spherical electron _e_ of radius _a_ be flying at moderate speed _u_, so that the magnetic field at any point, _rθ_, outside, is H = eu sinθ / r², and the energy per unit volume everywhere is μH²/8π. But a magnetic field has been thought of by many mathematicians as a circulation of fluid along the lines of magnetic induction--which are always closed curves--at some unknown velocity _w_. So consider the energy per unit volume anywhere: it can be represented by the equivalent expressions ½ρw² = μH²/8π = μ/8π · e²u²sin²θ / r²; wherefore w/u = √(μ/4πρ) · e sinθ / r². The velocity of the hypothetical circulation must be a maximum at the equator of the sphere, where r=a and θ=90; so, calling this _w₀_, w₀/u = √(μ/4πρ) e / a², and w/w₀ = a² sinθ / r²; wherefore the major part of the circulation is limited to a region not far removed from the surface of the electron. The energy of this motion is ½ρ ∫{0,π} ∫{a,∞} w² · 2π r sin θ · rdθ · dr, whence, substituting the above value of _w_, the energy comes out equal to 4/3 πρa³ w₀². Comparing this with a mass moving with speed _u_, m = 8/3 πρa³(w₀/u)². This agrees with the simple hydrodynamic estimate of effective inertia if w₀ = ½√3·u; that is to say, if the whirl in contact with the equator of the sphere is of the same order of magnitude as the velocity of the sphere. Now for the real relation between _w₀_ and _u_ we must make a hypothesis. If the two are considered equal, the effectively disturbed mass comes out as twice that of the bulk of the electron. If _w₀_ is smaller than _u_, then the mass of the effectively disturbed fluid is less even than the bulk of an electron; and in that case the estimate of the fluid-density ρ must be _exaggerated_ in order to supply the required energy. It is difficult to suppose the equatorial circulation _w₀_ _greater_ than _u_, since it is generated by it; and it is most reasonable to treat them both as of the same order of magnitude. So, taking them as equal, e = a² √(4πρ/μ) and m = twice the spherical mass. Hence all the estimates of the effective inertia of an electron are of the same order of magnitude, being all comparable with that of a mass of ether equal to the electron in bulk. But the linear dimension of an electron is 10⁻¹³ centimetre diameter, and its mass is of the order 10⁻²⁷ gram. Consequently the density of its material must be of the order 10¹² grams per cubic centimetre. This, truly, is enormous, but any reduction in the estimate of the circulation-speed, below that of an electron, would only go to increase it. And, since electrons move sometimes at a speed not far below that of light, we cannot be accused of under-estimating the probable velocity of magnetic spin by treating it as of the same order of magnitude, at the bounding surface of the electron, as its own speed: a relation suggested, though not enforced, by gyrostatic analogies. _Some Consequences of this Great Density._