The Ether of Space

by Sir Oliver Lodge

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 · e²u² sin²θ / 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 / wₒ = a² sinθ / r²