Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/382

 perpendicular to the radius from the centre, where di depends at any instant only on the distance from the vibrator, and 0 denotes the angle which the radius makes with the axis of the oscillator. At points on the axis, and in the equatorial plane, the electric force is parallel to the axis. At a great distance from the oscillator, is small compared with, so the wave is purely transverse. The magnetic force is directed along circles whose centres are on the axis of the radiator; and its magnitude may be represented in the form, where depends only on  and ; at great distances from the radiator,  is approximately equal to.

If the activity of the oscillator be supposed to be continually maintained, so that there is no damping, we may replace, by zero, and may proceed as in the case of the magnetic oscillator to determine the amount of energy radiated. The mean outward flow of energy per unit time is found to be ; from which it is seen that the rate of loss of energy by radiation increases greatly as the wave-length decreases.

The action of an electrical vibrator may be studied by the aid of mechanical models. In one of these, devised by Larmor, the aether is represented by an incompressible elastic solid, in which are two cavities, corresponding to the conductors of the vibrator, filled with incompressible fluid of negligible inertia, The electric force is represented by the displacement of the solid. For such rapid alternations as are here considered, the metallic poles behave as perfect conductors; and the tangential components of electric force at their surfaces are zero, This condition may be satisfied in the model by supposing the lining of each cavity to be of flexible sheet-metal, so as to be incapable of tangential displacement; the normal displacement of the lining then corresponds to the surface-density of electric charge on the conductor.

In order to obtain oscillations in the solid resembling those of an electric vibrator, we may suppose that the two cavities