Models Of The Aether

The early attempts of Thomson and Maxwell to represent the electric medium by mechanical models opened up a new field of research.

Two groups of models arose:

1. Linear electric force & electric current and a rotatory magnetism

This is in Thomson’s 1847 memoir[1] and Maxwell’s 1861 memoir[2].

2. Linear magnetic force and rotary electric current

This was devised by Maxwell in 1855[3] and afterwards amplified by Helmholtz[4].

In Maxwell’s analogy of 1861-2, a continuous vortical motion happens around the lines of magnetic induction.

Thomson’s Model

In Thomson’s analogy, the vector-potential was like the displacement in an elastic solid.

In this way, the magnetic induction at any point would be represented by the twist of an element of volume of the solid from its equilibrium position.

In symbols:

a = e, E = -e, B = curl e

• a is the vector-potential
• E the electric force
• B the magnetic induction
• e the elastic displacement

In 1890, Thomson showed that in his model, a linear current could be represented by a piece of endless cord.

• This cord was of the same quality as the solid and embedded in it, if a tangential force were applied to the cord uniformly all round the circuit.

The forces so applied tangentially produce a tangential drag on the surrounding solid.

The rotatory displacement thus caused is everywhere proportional to the magnetic vector.

In order to represent the effect of varying permeability, Thomson abandoned the ordinary type of elastic solid.

• He replaced it by an aether of MacCullagh’s type – an ideal incompressible substance
• This has no ordinary rigidity (i.e. elastic resistance to change of shape).
• It can resist absolute rotation.
  • This property was called ‘gyrostatic rigidity’

The rotation of the solid represented the magnetic induction

• The coefficient of gyrostatic rigidity was inversely proportional to the permeability of the magnetic induction.
• The normal component of magnetic induction will be continuous across an interface, as it should be.

In models of this kind, the electric force is represented by the translatory velocity of the medium.

It might therefore be expected that a strong electric field would perceptibly affect the speed of light.

Maxwell’s Model

The alternative was that:

• electric phenomena are rotatory
• magnetic force is the linear velocity of the medium

In symbols:

…

• D denotes the electric displacement
• H the magnetic force
• e the displacement of the medium

In Maxwell’s memoir of 1855 attention was directed chiefly to magnetic fields of a steady, or at any rate non-oscillatory, character.

In such fields, the motion of the particles of the medium is continuously progressive.

Consequently, the medium was fluid.

Maxwell later abandoned this idea in favour of rotatory magnetism.

According to Ampère:

• electric currents are a kind of translation
• magnetic force depends on rotation I agree, because the electric current is associated with electrolysis, and other undoubted instances of translation. Magnetism is associated with the rotation of the plane of polarization of light.

Maxwell

If the analogy has any dynamical (as distinguished from a merely kinematical) value, then the ponderomotive forces between metallic rings carrying electric currents should be similar to the ponderomotive forces between the same rings when they are immersed in an infinite incompressible fluid.

The motion of the fluid being such that its circulation through the aperture of each ring is proportional to the strength of the electric current in the corresponding ring.

Kirchhoff solved the hydrodynamical problem of the motion of 2 thin, rigid rings in an incompressible frictionless fluid, the fluid motion being irrotational.

He found that the forces between the rings are numerically equal to those which the rings would exert on each other if they were traversed by electric currents proportional to the circulations.

There is, however, an important difference between the 2 cases.