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 position at the time T and for radius the path passed over by light during the time t.

Lorentz has given in this way the expressions for the two electric and vector potentials from which the fields can be deduced by the well-known formula. The complete expressions for these fields have been given for the first time, I believe, by Lenard; I obtained them independently at the same time as Schwartzschild by putting them in the following form.

The expressions for the two fields consist of two parts: the first depends solely on the velocity of the element at the time T and contributes to form the wake (sillage) which accompanies the electron in its motion; I shall call this the velocity wave. This velocity wave, which exists only in the case of uniform motion, has its electric field always directed toward the position which the element of charge will occupy at the time T + t, if it had retained from the time T the velocity which it had at that moment. Schwartzschild calls this position the point of aberration. It coincides with the true position of the moving element at time T if the motion has been uniform. The other part of the two fields is proportional to the acceleration projected on the direction of propagation, and the directions of the two fields are there perpendicular to one another, and perpendicular to the radius, at the same time the two electric and magnetic fields represent equal energies per unit volume; they have all the characteristics of a radiation which is freely propagated in the ether. I shall call this part the acceleration wave. Moreover, the intensities of the fields in this case vary inversely as the distance from the centre of emission, the energy represented by this wave does not tend toward zero as the time T increases indefinitely; there is thus energy radiated to infinity by the acceleration wave.

The velocity wave, on the contrary, in which the fields vary inversely as the square of the radius Vt, does not carry any energy to infinity: the energy of the velocity wave accompanies the electron in its motion and corresponds to its kinetic energy.

(16) Radiation implies Acceleration. We can conclude from this that when an electrified centre experiences an acceleration, and only then, it radiates to infinity in the form of a transverse wave, electromagnetic radiation, a definite quantity of energy, proportional per unit of time to the square of the acceleration.

The origin of electromagnetic radiation, of all radiation, is, then, in the electron undergoing acceleration. It is through the electron that matter acts as the source of Hertzian or light waves. All acceleration, all change which takes place in the state of motion of electrons, result in the emission of waves. The character of the emitted waves changes naturally according as the acceleration is abrupt, discontinuous, or periodic.