The advancing front of the train of waves emitted by a theoretical Hertzian oscillator.

The waves emitted by Hertz’s oscillator have been identified with those due to a vibrating electric doublet, that is to say, to a singular point (of a certain type) of the electromagnetic equations. In air or in free æther these equations may be written in the forms 1/c ∂/∂t (X, Y, Z) = curl (α, β, γ ) } —1/c ∂/∂t (α, β, γ ) = curl (X, Y, Z) } . . . . (1), in which c is the velocity of radiation, (X, Y, Z) denotes the electric force measured in electrostatic units, (α, β, γ ) denotes the magnetic force measured in electromagnetic units. These equations are nearly identical with those which have been used by Hertz. They differ from the latter in that c is here written for the quantity which Hertz wrote 1/A, and they differ also in the signs of the right-hand members. The reason for the latter difference is that Hertz used a left-handed system of axes ofx, y, z ; but it is on many grounds more convenient to use a right-handed system, as will be done here.