Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/475

 and propagated parallel to the axis of, the electric vector being parallel to the axis of. Thus the equations of motion reduce to

For, and we may substitute exponential functions of

where denotes the frequency of the light, and  the quasi-index of refraction of the metal: the equations then give at once

Writing $$\nu (1 -\kappa\sqrt{-1})$$ for, so that is inversely proportional to the velocity of light in the medium, and  denotes the coefficient of absorption, and equating separately the real and imaginary parts of the equation, we obtain

When the wave-length of the light is very large, the inertia represented by the constant has but little influence, and the equations reduce to those of Maxwell's original theory of the propagation of light in metals. The formulae were experimentally confirmed for this case by the researches of E. Hagen and H, Rubens with infra-red light; a relation being thus established between the ohmic conductivity of a metal and its optical properties with respect to light of great wavelength.

When, however, the luminous vibrations are performed more rapidly, the effect of the inertia becomes predominant; and