Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/328

 Maxwell further assumed that the current thus produced interacts dynamically with the luminous motion in such a manner that the kinetic energy of the medium contains a term proportional to the scalar product of ė and curl &part;e/&part;θ. The total kinetic energy of the medium may therefore be written

where p denotes the density of the medium, and o denotes a constant which measures the capacity of the medium to rotate the plane of polarization of light in a magnetic field.

The equation of motion may now be derived as in the elastic-solid theories of light: it is

When the light is transmitted in the direction of the lines of force, and the axis of x is taken parallel to this direction, the equation reduces to

and these equations, as we have seen, furnish an explanation of Faraday's phenomenon.

It may be remarked that the term

in the kinetic energy may by partial integration be transformed into a term

together with surface-terms; or, again, into

together with surface-terms. These different forms all yield