RELATIONS TO OTHER SCIENCES 133 



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 elec- 

 tron in its motion; I shall call this the velocity wave. This velocity 

 wave, which exists only in the case of uniform motion, has its elec- 

 tric 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, electro- 

 magnetic 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, dis- 

 continuous, or periodic. 



